How do you simplify $\frac{200}{\sqrt{5}}$ $200/sqrt5$ ?

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Answer 1 · 2018-03-10T01:15:44

The result is $40 \sqrt{5}$ $40sqrt5$ .

Factor $200$ $200$ , separate the fraction, then combine the exponents:

$\frac{200}{\sqrt{5}}$ $color(blue)200/sqrt5$

$\frac{200}{5^{\frac{1}{2}}}$ $color(blue)200/(5^(1/2))$

$200 \cdot \frac{1}{5^{\frac{1}{2}}}$ $color(blue)200*1/(5^(1/2))$

$200 \cdot 5^{- \frac{1}{2}}$ $color(blue)200*5^(-1/2)$

$40 \cdot 5 \cdot 5^{- \frac{1}{2}}$ $color(blue)(40*5)*5^(-1/2)$

$40 \cdot 5^{1} \cdot 5^{- \frac{1}{2}}$ $color(blue)(40*5^1)*5^(-1/2)$

$40 \cdot 5^{1 - \frac{1}{2}}$ $color(blue)40*5^(1-1/2)$

$40 \cdot 5^{\frac{1}{2}}$ $color(blue)40*5^(1/2)$

$40 \cdot \sqrt{5}$ $color(blue)40*sqrt5$

$40 \sqrt{5}$ $color(blue)40sqrt5$

How do you simplify 200√5200/sqrt5?