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olmalıdır.","Köklü ifadelerde payda sıfır olamaz, bu da çözüme etki edebilir."]},"beginTime":279,"endTime":554,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=279&ask_summarization=1"},{"index":4,"title":"Köklü İfadelerin Özelliklerinin Uygulanması","list":{"type":"unordered","items":["Köklü ifadelerde kök dışına çıkarma işlemi yapılırken, kökün derecesi ile üstün derecesi aynıysa birbirini götürür ve içteki ifade dışarı çıkar.","Tek dereceli köklü ifadelerde içteki ifade direkt dışarı çıkar, çift dereceli köklü ifadelerde ise mutlak değer dışarı çıkar.","Çift dereceli köklü ifadelerde mutlak değer dışarı çıkarıldığından, sonucun her zaman pozitif olması 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Yazma","list":{"type":"unordered","items":["Matematikte önemli olan bir kuralı bilmek değil, düzgün yazmak ve tersten okumaktır.","Tersten okuma, nasıl dışarı çıktığını düşünerek içeriye yerleştirme işlemidir (örneğin, a üzeri en dışarı çıkıyorsa, içeriye a üzeri en olarak girer).","Kök içindeki sayıları kare, küp veya diğer kuvvetler olarak yazarak dışarı çıkarma işlemi yapılabilir (örneğin: 18 = 9×2, 72 = 36×2)."]},"beginTime":886,"endTime":1142,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=886&ask_summarization=1"},{"index":7,"title":"Köklü Sayıların Üslü Sayı Şeklinde Yazımı","list":{"type":"unordered","items":["Her köklü sayı aynı zamanda bir üslü sayıdır.","Kök işaretinin üst üste yazılması, üslü sayı şeklinde yazımın temelidir (örneğin: ³√252 = 252^(1/3)).","Üslü sayı şeklinde yazım, tabanlar aynıysa üstlerin toplanması veya çıkarılması gibi işlemlerde kolaylık sağlar."]},"beginTime":1142,"endTime":1378,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1142&ask_summarization=1"},{"index":8,"title":"Kök Derecelerinin Genişletilmesi ve Sadeleştirilmesi","list":{"type":"unordered","items":["Kök derecesi genişletilebilir veya sadeleştirilebilir, ancak içeriğin de aynı şekilde genişletilmesi veya sadeleştirilmesi gerekir.","Kök derecelerinin eşitlenmesi, sıralama sorularında ve iç içe köklerde kullanışlıdır.","Kök içindeki üst 1 ve kök derecesi 2 olduğunda, bunlar yazılmaz (örneğin: √a = a^(1/2))."]},"beginTime":1378,"endTime":1501,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1378&ask_summarization=1"},{"index":9,"title":"Sıralama Sorularında Kök Derecelerinin Eşitlenmesi","list":{"type":"unordered","items":["Sıralama sorularında, köklerin tabanları eşitlenir veya dereceleri eşitlenir.","Kök derecelerini eşitlemek için, her kökün derecesini aynı sayıya genişletmek gerekir (örneğin: ²√a, ³√b, ⁴√c'yi ¹²√a, ¹²√b, ¹²√c şeklinde eşitlemek).","Dereceleri eşitlendikten sonra, kök içindeki sayılar karşılaştırılarak sıralama yapılır."]},"beginTime":1501,"endTime":1587,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1501&ask_summarization=1"},{"index":10,"title":"Köklü İfadelerde Toplama ve Çıkarma","list":{"type":"unordered","items":["Köklü ifadelerde toplama ve çıkarma işlemi yapılırken, kök kuvveti ve içi aynı olan terimler toplanıp çıkarılır.","Kök kuvveti veya içi farklı olan terimler toplanamaz veya çıkarılamaz.","Köklü ifadelerde toplama ve çıkarma işlemi, üslü sayılarda olduğu gibi aynı terimlerin toplanması gibidir."]},"beginTime":1592,"endTime":1889,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1592&ask_summarization=1"},{"index":11,"title":"Köklü İfadelerde Çarpma ve Bölme","list":{"type":"unordered","items":["Kök kuvvetleri aynı olan köklü ifadeler çarpılır veya bölünürken, kök içine girerler ve çarpılırlar.","Kök kuvvetleri farklı olan ifadeler çarpılırken önce kök kuvvetleri eşitlenir.","Kök kuvvetlerini eşitlemek için, kökün derecesi ile genişletme yapılır ve içteki sayılar da aynı oranda çarpılır."]},"beginTime":1889,"endTime":2065,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1889&ask_summarization=1"},{"index":12,"title":"Eşlilik Kavramı","list":{"type":"unordered","items":["Eşlilik kavramı, köklü ifadeleri kökten kurtarmak için kullanılır.","Köklü ifadeleri eşliliği ile çarptığımızda, iki kare farkı formülü kullanılarak kökten kurtulur.","Bir köklü ifadenin eşlisi, kök içindeki ifadenin işaretini değiştirerek bulunur (örneğin, kök x - kök y'nin eşlisi kök x + kök y'dir)."]},"beginTime":2065,"endTime":2248,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2065&ask_summarization=1"},{"index":13,"title":"Köklü Sayıların Eşleniği","list":{"type":"unordered","items":["Köklü sayıların kökten kurtarılması için eşlenik çarpımı yapılır.","Kök beş eksi kök üç ile kök beş artı kök üç çarpıldığında, kökler birbirini götürüp sayılar kalır.","Köklü sayıların eşlenik çarpımı a²-b² formülüne göre hesaplanır."]},"beginTime":2252,"endTime":2307,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2252&ask_summarization=1"},{"index":14,"title":"Köklü Sayıların Çarpımı","list":{"type":"unordered","items":["Köklü sayıların çarpımı a²-b² formülüne göre hesaplanır.","Köklerin karesi alınarak sonuç bulunur.","Köklü sayıların çarpımında genellikle terimler birbirini götürür."]},"beginTime":2307,"endTime":2384,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2307&ask_summarization=1"},{"index":15,"title":"Köklü Sayıların Kökten Kurtarılması","list":{"type":"unordered","items":["Köklü sayıların kökten kurtarılması için eşlenik çarpımı yapılır.","Pay ve payda eşlenikle çarpılır, kökler birbirini götürür.","Sonuçta köklü sayılar sadeleştirilir."]},"beginTime":2384,"endTime":2465,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2384&ask_summarization=1"},{"index":16,"title":"Kök İçinde Muhabbetler","list":{"type":"unordered","items":["Kök içinde muhabbetler üslü sayılara benzer şekilde işlem yapılır.","Kök kök içinde sayı yoksa, dereceler çarpılarak tek kök içinde ifade edilir.","Kök kök içinde sayı varsa, içeri girerken üs alınarak işlem yapılır."]},"beginTime":2465,"endTime":2655,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2465&ask_summarization=1"},{"index":17,"title":"Kök İçinde Muhabbet Örnekleri","list":{"type":"unordered","items":["Kök içinde muhabbetlerde dışarıdaki kökler içeri girerken üs alınır.","Dereceler çarpılarak tek kök içinde ifade edilir.","Kök içindeki sayılar çarpılarak tek kök içinde ifade edilir."]},"beginTime":2655,"endTime":2801,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2655&ask_summarization=1"},{"index":18,"title":"Köklü Sayıların Kareleri","list":{"type":"unordered","items":["(a+b)² formülü hatırlatılıyor: birinci terimin karesi, iki terimin çarpımının iki katı ve ikinci terimin karesi toplamı.","Örnek olarak (√3+√2)² hesaplanıyor: 3+2√6+2=5+2√6.","İki köklü sayının karesi alınırken, sonuç iki sayının toplamı ve çarpımı şeklinde ifade edilir."]},"beginTime":2803,"endTime":2899,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2803&ask_summarization=1"},{"index":19,"title":"Köklü Sayıların Çözümü","list":{"type":"unordered","items":["x=iki sayının toplamı ve y=iki sayının çarpımı şeklindeki ifadelerde, kök içindeki ifade köklü sayıların karesi olarak yazılabilir.","İşlemdeki \"2\" terimi çok önemlidir, bu terim görünce çözümü tamamlamak mümkündür.","Örnek olarak 5+2√6 ifadesi √3-√2 şeklinde yazılabilir."]},"beginTime":2899,"endTime":2983,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2899&ask_summarization=1"},{"index":20,"title":"Örnek Sorular","list":{"type":"unordered","items":["İzleyicilere 11+2√18 ifadesini çözmeleri isteniyor.","Çözüm: 9+2=11 ve 9×2=18 olduğundan, ifade √9+√2 şeklinde yazılır.","Köklü sayılar canlı yayını burada sona eriyor ve izleyicilerden cevaplarını yorumlara bırakmaları isteniyor."]},"beginTime":2983,"endTime":3053,"href":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=2983&ask_summarization=1"}],"linkTemplate":"/video/preview/8895756362113893670?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"9. 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Öğretmen, \"Yer ve Zaman\" ünitesinin bir parçası olan coğrafi koordinat sistemi konusunu anlatmaktadır.","Video, coğrafi koordinat sisteminin temel kavramlarını sistematik olarak ele almaktadır. İlk olarak kutup ve ekvator kavramları, paraleller ve meridyenler tanıtılmakta, ardından enlem kavramı ve enlem etkisi detaylı şekilde açıklanmaktadır. Daha sonra meridyenler, yerel saat, saat dilimleri, Greenwich meridyeni, tarih değiştirme çizgisi ve anti-meridyen kavramları anlatılmaktadır.","Videoda kitaptan 36-38. sayfaları kapsamakta ve konular görsel örneklerle desteklenmektedir. Ayrıca, enlem etkisinin bitki örtüsü, denizlerin tuzluluğu, basınç alanları ve sıcaklık gibi konulardaki etkileri örneklerle açıklanmakta, yerel saat hesaplamaları ve zaman farkı hesaplamaları örneklerle pekiştirilmektedir. Video, öğrencilere ödevlendirme ve ödüllü soru ile sonlanmaktadır."]},"endTime":1850,"title":"Coğrafi Koordinat Sistemi ve Saat Dilimleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Coğrafi Koordinat Sistemi Konusuna Giriş","list":{"type":"unordered","items":["Uzaktan eğitimle coğrafi koordinat sistemi konusu işlenecek.","Ünite içeriğinde yer ve zaman, paralel enlem, meridyen, boylam ve yerel saat kavramları ele alınacak.","Bir sonraki derste yer ve zaman ünitesi tamamlanacak, Türkiye'nin coğrafi konumu öğrenilecek."]},"beginTime":1,"endTime":101,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1&ask_summarization=1"},{"index":1,"title":"Koordinat Sisteminin Temel Kavramları","list":{"type":"unordered","items":["Koordinat sistemi, dünya üzerindeki herhangi bir yerin konumunu ve zaman-yere ait özelliklerini belirlemek için oluşturulmuştur.","Kutup, dünyanın kendi ekseni etrafındaki hareketi sırasında dönmeyen hareketsiz noktalardır; 90 derece kuzey enlemi kuzey kutup noktasını, 90 derece güney enlemi ise güney kutup noktasını oluşturur.","Ekvator, dünyayı kuzey ve güney olmak üzere iki eşit kısma ayıran, doğu-batı yönlü uzanan en geniş paralel dairesidir ve 0 derece enlemdir."]},"beginTime":101,"endTime":168,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=101&ask_summarization=1"},{"index":2,"title":"Paralellerin Özellikleri","list":{"type":"unordered","items":["Paraleller, ekvatora bir derece aralıklarla çizilen dairelerdir ve toplam 180 tane paralel dairesi bulunmaktadır.","Ekvatorun kuzeyinde çizebileceğimiz toplam 90 tane, güneyinde de çizebileceğimiz 90 tane paralel dairesi vardır.","Paraleller hiçbir zaman birbirlerini kesmezler, aralarındaki kuş uçuşu mesafe sabittir ve 111 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başlangıç paraleline olan uzaklığının açı cinsinden ifadesine enlem denir.","Enlem, derece, dakika ve saniye cinsinden ifade edilir; örneğin Ankara'nın enlemi 39 derece 57 dakika kuzey enlemidir.","Her paralel derecesi bir enlemdir ama her enlem bir paralel değildir."]},"beginTime":555,"endTime":641,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=555&ask_summarization=1"},{"index":5,"title":"Enlem Etkisi","list":{"type":"unordered","items":["Enlem etkisi, ekvatordan kutuplara doğru gidildikçe meydana gelen değişimlerdir ve güneş ışınlarının geliş açısına bağlıdır.","Güneş ışınlarının geliş açısı ekvatordan kutuplara doğru gidildikçe daralır, bu nedenle cisimlerin gölge boyları uzar.","Sıcaklık değerleri, deniz ve okyanuslardaki buharlaşma miktarı, tuzluluk oranı ve kalıcı kar alt sınırı ekvatordan kutuplara doğru gidildikçe azalır."]},"beginTime":641,"endTime":765,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=641&ask_summarization=1"},{"index":6,"title":"Bitki Örtüsü ve Ekonomik Etkinlikler","list":{"type":"unordered","items":["Bitki örtüsü kuşaklar oluşturur: ekvator çevresinde geniş yapraklı ormanlar, orta kuşak çevresinde karma yapraklı ormanlar, kutup altı alanlarında iğne yapraklı ormanlar ve tundralar bulunur.","Ekvatordan kutuplara doğru gidildikçe ekonomik etkinlikler ve faaliyetler değişir."]},"beginTime":765,"endTime":789,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=765&ask_summarization=1"},{"index":7,"title":"Enlem Etkisi","list":{"type":"unordered","items":["Enlem etkisiyle açıklanabilir durumlar: Brezilya'da geniş yapraklı ağaçlar, Umman Denizi'nin Baltık Denizinden daha tuzlu olması, Kongo Havzasında termik alçak basınç görülmesi.","Enlem etkisine ters düşen durumlar: Londra'nın Ottova'dan sıcak olması, Ocak ayında Avustralya'nın ekvatordan daha sıcak olması, Sibirya'nın kuzey kutbundan soğuk olması.","Enlem etkisiyle açıklanabilir durumlar: Arabistan'da daimi kar sınırının Kanada'dan yüksek olması, Grönland'da yerçekiminin Türkiye'den fazla olması, Türkiye'de güneş ışınlarının tutulma oranının Endonezya'dan fazla olması."]},"beginTime":793,"endTime":1004,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=793&ask_summarization=1"},{"index":8,"title":"Meridyenler","list":{"type":"unordered","items":["Meridyen, iki kutup noktası arasında uzanan paralel dairelerin dik kesen hayali yarım dairelerdir ve başlangıç meridyeni İngiltere'nin Greenge kasabasından geçer.","Meridyenler paraleller gibi bir derece aralıklarla çizilmiştir ve aynı sayısal değerden iki tane olduğu için yön belirtilmelidir.","Başlangıç meridyenin sol tarafında batı yarım küre, sağ tarafında doğu yarım küre bulunur ve her yarım kürede toplam 180 meridyen yayı vardır."]},"beginTime":1004,"endTime":1096,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1004&ask_summarization=1"},{"index":9,"title":"Meridyenlerin Özellikleri","list":{"type":"unordered","items":["Aynı meridyen üzerindeki bütün noktaların yerel saatleri aynıdır ve tüm meridyenlerin uzunlukları birbirine eşittir.","Ardışık iki meridyen arasındaki yerel saat farkı dört dakikadır çünkü dünya kendi ekseni etrafındaki bir tam turunu 24 saatlik sürede tamamlar ve 360 meridyeni geçer.","Dünya üzerindeki herhangi bir yerin başlangıç meridyeni uzaklığının açı cinsinden değeridir ve Ankara 32 derece 53 dakika 15 saniye doğu boylamında yer 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Kavramı","list":{"type":"unordered","items":["Ulusal saat ve uluslararası saat kavramları vardır, ayrıca ortak saat kavramı da bulunmaktadır.","Dünyayı 24 saat dilimini ayırır, doğusuna artı saat dilimleri, batısına ise eksi saat dilimleri denir.","Her 15 derecelik meridyen yayları (boylam dereceleri) o alanın ortak saat ayar boylamıdır."]},"beginTime":1286,"endTime":1359,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1286&ask_summarization=1"},{"index":12,"title":"Saat Dilimlerinin Belirlenmesi","list":{"type":"unordered","items":["Saat dilimlerinin belirlenmesi için Greenwich'in (0°) 7°30' doğusu ve batısı sıfırıncı ulusal saat dilimini oluşturur.","15° merkez boylamının 7°30' doğusu ve batısı bir ulusal saat dilimini oluşturur.","Ortak saat kavramı bu şekilde belirlenmiştir."]},"beginTime":1359,"endTime":1428,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1359&ask_summarization=1"},{"index":13,"title":"Tarih Değiştirme Çizgisi ve Anti-Meridyen","list":{"type":"unordered","items":["Tarih değiştirme çizgisi 180° meridyeninden (sıfırın anti-meridyeninden) geçer.","Anti-meridyen, bir meridyen yayını tam daire (180°) tamamlayan karşı yarım küredeki dairesidir.","Tarih değiştirme çizgisinin batısında (doğu yarım kürede) gün bir gün ileri, doğusunda (batı yarım kürede) gün bir gün geridir."]},"beginTime":1428,"endTime":1475,"href":"/video/preview/7288770454586455661?parent-reqid=1769930302605198-11821049069659323716-balancer-l7leveler-kubr-yp-vla-91-BAL&text=kittyex9&t=1428&ask_summarization=1"},{"index":14,"title":"Soru Çözümü","list":{"type":"unordered","items":["Ekvator üzerinde yer alan merkezlerin paralel dereceleri ortaktır ve ekvatora kuş 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