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math question
2√2×√32​

Answer 1

Answer:

$2 \times \sqrt{2} \times \sqrt{32} \\ = 2 \times \sqrt{2} \times \sqrt{2 \times 2 \times 2 \times 2 \times 2} \\ = 2 \times \sqrt{2} \times 2 \times 2 \times \sqrt{2} \\ = 2 \times 2 \times 2 \times \sqrt{2 } \times \sqrt{2} \\ = 2 \times 2 \times 2 \times 2 \\ = 16$

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Answer 2

$\leadsto\tt\purple{Question:-}$

$\purple\leadsto \small \tt{2 \sqrt{2} \times \sqrt{32} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\leadsto\tt{Solution:-}$

$\leadsto\small\tt \purple{First \: do \: Prime \: Factorisation \: of \: 32}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\small \begin{array}{r|l}2&32\\ 2&16\\2&8\\2&4\\2&2\\&1\end{array}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple\leadsto \small \tt{2 \sqrt{2} \times \sqrt{32} }$

$\purple \leadsto \small \tt{2 \sqrt{2} \times \sqrt{2 \times 2 \times 2 \times 2 \times 2} }$

$\purple\leadsto \small \tt{2 \sqrt{2} \times \sqrt{2 \underbrace\times 2 \times2 \underbrace \times 2 \times 2} }$

$\purple\leadsto \small \tt{2 \sqrt{2} \times2 \times 2\sqrt{2} }$

$\purple \leadsto \small \tt{2 \sqrt{2} \times4\sqrt{2} }$

$\purple \leadsto\small \tt{2 \times 4 \times ({ \sqrt{2} })^{2} }$

$\purple \leadsto \small \tt{2 \times 4 \times \cancel { \sqrt{2} }^{ \cancel2} }$

$\purple\leadsto \small \tt{2 \times 4 \times 2 }$

$\leadsto \small \tt \purple{16 }$