How do you simplify $\sqrt{\frac{400}{5}}$ $sqrt(400/5)$ ?

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How do you simplify $\sqrt{\frac{400}{5}}$ $sqrt(400/5)$ ?

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Answer 1 · 2018-03-15T18:23:21

See below.

Explanation:

$\sqrt{\frac{400}{5}} = \frac{\sqrt{400}}{\sqrt{5}}$ $sqrt(400/5) = sqrt(400)/sqrt(5)$

$\frac{\sqrt{400}}{\sqrt{5}} = \frac{20}{\sqrt{5}}$ $sqrt(400)/sqrt(5)=20/sqrt5$

$= \frac{20}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$ $=20/sqrt(5) * sqrt(5)/sqrt(5)$

$= \frac{20 \sqrt{5}}{5} = 4 \sqrt{5}$ $=(20sqrt(5))/5 = 4sqrt5$

Answer 2 · 2018-03-15T18:24:30

$\sqrt{\frac{400}{5}} = 4 \sqrt{5}$ $sqrt(400/5)=4sqrt(5)$

Explanation:

$\sqrt{\frac{400}{5}} = \frac{\sqrt{400}}{\sqrt{5}} = \frac{20}{\sqrt{5}}$ $sqrt(400/5)=sqrt(400)/sqrt(5)=20/sqrt(5)$

We want to rationalize the denominator. Here we are just getting rid of the square root, shown in blue.

$\frac{20}{\sqrt{5}} = \frac{20 \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{20 \sqrt{5}}{5} = 4 \sqrt{5}$ $20/sqrt(5)=(20color(blue)(sqrt(5)))/(sqrt(5)*color(blue)(sqrt(5)))=(20sqrt5)/5=4sqrt(5)$

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