What is the square root of 64/125?

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Answer 1 · 2018-04-24T13:25:42

0.7155417528

$(\frac{64}{125}) = 0.512$ $(64/125)=0.512$

$\sqrt{0.512}$ $sqrt(0.512)$

=0.7155417528

with 2 significant figures= 0.72

with 3 significant figures= 0.716

Answer 2 · 2018-04-24T14:59:54

$\frac{8}{5 \cdot \sqrt{5}}$ $color(blue)((8)/(5*sqrt(5)$

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Simplify $\sqrt{\frac{64}{125}}$ $color(red)(sqrt(64/125)$

Rewrite the expression as $\frac{\sqrt{64}}{\sqrt{125}}$ $color(red)(sqrt(64)/sqrt(125)$

$64 = 16 \cdot 4$ $64=16*4$

$125 = 25 \cdot 5$ $125=25*5$

Using these equivalents,

Rewrite the expression $\frac{\sqrt{64}}{\sqrt{125}}$ $color(red)(sqrt(64)/sqrt(125)$ as

$\frac{\sqrt{16.4}}{\sqrt{25 \cdot 5}}$ $color(blue)(sqrt(16.4)/sqrt(25*5)$

$\Rightarrow \frac{\sqrt{16} \cdot \sqrt{4}}{\sqrt{25} \cdot \sqrt{5}}$ $rArr (sqrt(16)*sqrt(4))/(sqrt(25)*sqrt(5)$

$\Rightarrow \frac{4 \cdot 2}{5 \cdot \sqrt{5}}$ $rArr (4*2)/(5*sqrt(5)$

$\Rightarrow \frac{8}{5 \cdot \sqrt{5}}$ $rArr 8/(5*sqrt(5)$

Hence, $\frac{\sqrt{64}}{\sqrt{125}} = \frac{8}{5 \sqrt{5}}$ $color(blue)(sqrt(64)/sqrt(125)=8/(5sqrt(5)$

Hope it helps.