# How do you simplify (5sqrt15) /( 3sqrt27) ?

Mar 11, 2016

Same thing. Just a very slightly different presentation!

$\frac{5 \sqrt{5}}{9}$

#### Explanation:

The answer given was stopped at $\frac{5 \sqrt{5}}{3 \sqrt{9}}$

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It is considered better mathematical practice if you 'get rid' of any roots that are in the denominator (bottom number)

The method is based on: Multiply any number by 1 and you do not change its inherent value

So $\frac{5 \sqrt{5}}{3 \sqrt{9}} \times 1$ does not change its value

Suppose we wrote 1 as $\frac{\sqrt{9}}{\sqrt{9}}$

This is still 1

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$\textcolor{b l u e}{\text{Back to solving the question}}$

Multiply by 1 but in the form of $\frac{\sqrt{9}}{\sqrt{9}}$ giving

$\frac{5 \sqrt{5}}{3 \sqrt{9}} \times \frac{\sqrt{9}}{\sqrt{9}} \text{ "=" } \frac{5 \sqrt{5} \sqrt{9}}{3 \sqrt{9} \sqrt{9}}$

$\frac{5 \sqrt{5} \sqrt{9}}{3 \times 9}$

But $\sqrt{9} = 3$ giving:

$\frac{5 \times 3 \times \sqrt{5}}{3 \times 9} \text{ "=" } \frac{3}{3} \times \frac{5 \sqrt{5}}{9}$

But $\frac{3}{3} = 1$ giving:

$\frac{5 \sqrt{5}}{9}$