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Öğretmen, Ferhat, Merve, Yağmur ve İbrahim gibi öğrencilerin de katıldığı bir ders ortamında sunum yapmaktadır.","Videoda köklü sayılar konusu detaylı bir şekilde ele alınmaktadır. Öğretmen, köklü ifadelerin özellikleri, kök dışına çıkarma kuralları, köklü sayıların üslü sayı şeklinde yazımı, kök derecelerinin genişletilmesi/sadeleştirilmesi, köklü ifadelerde toplama-çıkarma-çarpma-bölme işlemlerinin nasıl yapılacağı, köklü sayıların eşlenikleri ve kök içinde muhabbetler konularını örneklerle açıklamaktadır.","Video, 2. dönem sonu soru çözümlerini içeren interaktif bir ders formatında ilerlemektedir. Öğretmen, hastalıktan dolayı yorulduğunu belirterek izleyicilere özür dilerken, konuyu adım adım ve pratik örneklerle anlatmaktadır. Video, bir soru çözümüyle ve ödüllü bir soruyla sona ermektedir."]},"endTime":3073,"title":"9. Sınıf Köklü Sayılar Canlı Yayın Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"9. Sınıf Köklü Sayılar Konusuna Giriş","list":{"type":"unordered","items":["9. sınıf köklü sayılar konusunu anlatan canlı yayında öğrencilerle birlikteyiz.","Geçen canlı yayın çok interaktif ve etkili olmuş, bugün de güzel bir yayın sunulması hedefleniyor.","Köklü sayılar konusu çok önemli olduğu için dikkatli dinlemek gerekiyor."]},"beginTime":2,"endTime":82,"href":"/video/preview/8895756362113893670?parent-reqid=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&t=2&ask_summarization=1"},{"index":1,"title":"Köklü Sayıların Tanımı","list":{"type":"unordered","items":["n bir pozitif tam sayı ve a bir reel sayı olmak üzere, n ≥ 2 olacak şekilde x üzeri n = a denkleminin çözümü olan x gerçek sayılarına a sayısının n. dereceden kökü denir.","Köklü sayılar ortaokuldan bilinir ancak 9. sınıfta daha gelişmiş konular ele alınacak.","Kök içindeki sayı, kökün derecesine göre farklı sonuçlar verebilir; örneğin 64, 4'ün küpü (3. dereceden kök) veya 8'in karesi (2. 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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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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 gerekir."]},"beginTime":554,"endTime":741,"href":"/video/preview/8895756362113893670?parent-reqid=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&t=554&ask_summarization=1"},{"index":5,"title":"Kök Dışına Çıkarma","list":{"type":"unordered","items":["Kök dışına çıkarma işlemi yapılırken, kök içindeki sayıların kare, küp veya diğer kuvvetlerini bilmek önemlidir (örneğin: kök 4 = 2, kök 9 = 3, kök 16 = 4).","Küp kök dışına çıkarma işlemi yapılırken, kök içindeki sayının küpünü bilmek gerekir (örneğin: küp kök 27 = 3, küp kök 64 = 4).","Kök dışına çıkarma ikinci kuralı: Enişteden bir kök x varsa ve çarpanları ayrıldığında belirli bir formu alıyorsa, x üzeri en bey çıkarılır."]},"beginTime":749,"endTime":886,"href":"/video/preview/8895756362113893670?parent-reqid=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&t=749&ask_summarization=1"},{"index":6,"title":"Tersten Okuma ve Düzgün 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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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 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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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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 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iki sayının toplamı ve çarpımı şeklinde ifade edilir."]},"beginTime":2803,"endTime":2899,"href":"/video/preview/8895756362113893670?parent-reqid=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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=1769698333625820-9590301809055057320-balancer-l7leveler-kubr-yp-klg-270-BAL&text=tuck9&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 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