How do you simplify $\frac{25}{\sqrt{125}}$ $25/sqrt125$ ?

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How do you simplify $\frac{25}{\sqrt{125}}$ $25/sqrt125$ ?

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Answer 1 · 2017-05-30T17:12:15

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

Explanation:

$\frac{25}{\sqrt{125}}$ $25/sqrt(125)$

Let's rewrite the denominator.

$\frac{25}{(\sqrt{25}) (\sqrt{5})}$ $25/((sqrt(25))(sqrt(5)))$

Simplify

$\frac{25}{5 (\sqrt{5})}$ $25/(5(sqrt(5)))$

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

Rationalise the denominator

$= \frac{5}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$ $= frac(5)(sqrt(5)) cdot frac(sqrt(5))(sqrt(5))$

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

$= \sqrt{5}$ $= sqrt(5)$

Answer 2 · 2017-05-30T17:26:25

$\sqrt{5}$ $sqrt(5)$

Explanation:

We have: $\frac{25}{\sqrt{125}}$ $frac(25)(sqrt(125))$

Let's express the denominator as a product:

$= \frac{25}{\sqrt{5^{2} \cdot 5}}$ $= frac(25)(sqrt(5^(2) cdot 5))$

$= \frac{25}{5 \sqrt{5}}$ $= frac(25)(5 sqrt(5))$

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

Then, let's rationalise the denominator:

$= \frac{5}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$ $= frac(5)(sqrt(5)) cdot frac(sqrt(5))(sqrt(5))$

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

$= \sqrt{5}$ $= sqrt(5)$

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How do you simplify $\frac{25}{\sqrt{125}}$ $25/sqrt125$ ?

2 Answers

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