50 poin Wajib Pakai Cara.... Question from @Darrylchandra

December 2019 1 90 Report

$\sqrt{ 1 - \sqrt{ \frac{1 - \frac{1}{2} }{2}\sqrt{ \frac{1 - \frac{1}{2} }{2} \sqrt{ \frac{1 - \frac{1}{2} }{2} ... } } } } =$
50 poin Wajib Pakai Cara

mardanjefryoug9em

Verified answer

$\sqrt{1 - \sqrt{ \frac{1 - \frac{1}{2} }{2} \sqrt{ \frac{1 - \frac{1}{2} }{2} \sqrt{ \frac{1 - \frac{1}{2} }{2} } } } }$
Hitung selisih
$= \sqrt{1 - \sqrt{ \frac{ \frac{2 - 1}{2} }{2} \sqrt{ \frac{ \frac{2 - 1}{2} }{2} \sqrt{ \frac{ \frac{2 - 1}{2} }{2} } } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{ \frac{1}{2} }{2} \sqrt{ \frac{ \frac{1}{2} }{2} \sqrt{ \frac{ \frac{1}{2} }{2} } } } }$
Sederhanakan pecahannya

$= \sqrt{1 - \sqrt{ \frac{1}{2} \div 2 \sqrt{ \frac{1}{2 } \div 2 \sqrt{ \frac{1}{2} \div 2 } } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{1}{2} \times \frac{1}{2 } \sqrt{ \frac{1}{2} \times \frac{1}{2} \sqrt{ \frac{1}{2} \times \frac{1}{2} } } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{1}{4} \sqrt{ \frac{1}{4} \sqrt{ \frac{1}{4} } } } }$
Sederhanakan bentuk akarnya

$= \sqrt{1 - \sqrt{ \frac{1}{4} \sqrt{ \frac{1}{4} \times \frac{1}{2} } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{1}{4} \times \frac{1}{2} \sqrt{ \frac{1}{2} } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{1}{4} \times \frac{1}{2} \times \frac{1}{ \sqrt{2} } } }$
Kalikan

$= \sqrt{1 - \sqrt{ \frac{1}{8 \sqrt{2} } } }$
Rasionalkan

$= \sqrt{1 - \sqrt{ \frac{1 \times \sqrt{2} }{8 \sqrt{2} \times \sqrt{2} } } } \\ \\ = \sqrt{1 - \sqrt{ \frac{ \sqrt{2} }{8 \times 2} } } \\ \\ = \sqrt{1 - \sqrt{ \frac{ \sqrt{2} }{16} } } \\ \\ = \sqrt{1 - \frac{ \sqrt{ \sqrt{2} } }{4} } \\ \\ = \sqrt{1 - \frac{ \sqrt[4]{2} }{4} }$

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