# How do you simplify (9sqrt25)/sqrt50?

Apr 27, 2018

$\frac{9}{\sqrt{2}}$

#### Explanation:

$\frac{9 \sqrt{25}}{\sqrt{50}}$

$= \frac{9 \times 5}{\sqrt{50}}$

$\sqrt{50}$ can be simplified to $\sqrt{25 \times 2} = 5 \sqrt{2}$

$\frac{45}{5 \sqrt{2}}$

= $\frac{9}{\sqrt{2}}$

Apr 27, 2018

$\frac{9 \sqrt{2}}{2}$

#### Explanation:

$9 \sqrt{25}$ = $9 \times 5$ = 45

$\sqrt{50} = \sqrt{25} \times 2 = 5 \sqrt{2}$

so $\frac{9 \sqrt{25}}{\sqrt{50}} = \frac{45}{5 \sqrt{2}}$

dividing by top and bottom by 5 leaves

$\frac{9}{\sqrt{2}}$

If we multiply top and bottom by $\sqrt{2}$ this will rationalise it (remove the surd from the denominator)

$\frac{9}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$ =$\frac{9 \sqrt{2}}{2}$

Apr 27, 2018

$\frac{9 \sqrt{25}}{\sqrt{50}} = \frac{9 \sqrt{2}}{2}$

#### Explanation:

$\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$

So, $\frac{9 \sqrt{25}}{\sqrt{50}} = \frac{9 \sqrt{25}}{\sqrt{25} \cdot \sqrt{2}} = \frac{9}{\sqrt{2}}$

$\frac{9}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{9 \sqrt{2}}{2}$