Question

Bună! Ați putea să-mi spuneți cât da :
$\sqrt{2} \sqrt{3 \sqrt{6 \sqrt{5 \sqrt{9 \sqrt{21 \sqrt{5 \sqrt{3 \sqrt{9 \sqrt{4} } } } } } } } }$
​

Answer 1

Răspuns:

Explicație pas cu pas:

$\sqrt{2} \sqrt{3\sqrt{6\sqrt{5\sqrt{9\sqrt{21\sqrt{5\sqrt{3\sqrt{9\sqrt{4} } } } } } } } } =$

$=\sqrt{2} \sqrt{3\sqrt{6\sqrt{5\sqrt{9\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$=\sqrt{3*2\sqrt{6\sqrt{5\sqrt{9\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$=\sqrt{\sqrt{6^{2} \sqrt{5\sqrt{9\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{6^{4}* 5\sqrt{9\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{6^{8}* 5^{2}*9\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{3^{8}*2^{8}* 5^{2}*3^{2}\sqrt{21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{16}*2^{16}* 5^{4}*3^{4}*21\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{16}*2^{16}* 5^{4}*3^{4}*3*7\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{21}*2^{16}* 5^{4}*7\sqrt{5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{42}*2^{32}* 5^{8}*7^{2}*5\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{42}*2^{32}* 5^{9}*7^{2}\sqrt{3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{84}*2^{64}* 5^{18}*7^{4}*3\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{85}*2^{64}* 5^{18}*7^{4}\sqrt{3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{170}*2^{128}* 5^{36}*7^{8}*3^{2}*2 } } } } } } } } =$

$= \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{3^{172}*2^{129}* 5^{36}*7^{8} } } } } } } } } =$

$=\sqrt[256]{3^{172}*2^{129}* 5^{36}*7^{8}} =$

$={3^{\frac{172}{256} }*2^{\frac{129}{256} }* 5^{\frac{36}{256} }*7^{\frac{8}{256} } =$

$={3^{\frac{43}{64} }*2^{\frac{129}{256} }* 5^{\frac{9}{64} }*7^{\frac{1}{32 }$