# How do you simplify 5sqrt(1/3)?

Feb 22, 2016

So $5 \sqrt{\frac{1}{3}} \text{ "=" } \frac{5 \sqrt{3}}{3}$

I am not convinced this is a simplified version!

#### Explanation:

$5 \sqrt{\frac{1}{3}} \text{ " =" } 5 \frac{\sqrt{1}}{\sqrt{3}}$

But $\sqrt{1} = 1 \text{ technically it is } \pm 1$

$\frac{5}{\sqrt{3}} \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left(1\right)$

It is common mathematical practise to try and not have any roots in the denominator. If possible!

Note that if we have sqrt(3)/(sqrt(3)  it is the same value as 1

Multiply expression (1) by the value of 1 but in the form of$\text{ } \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{5}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \text{ "=" "(5sqrt(3))/3" } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

So $5 \sqrt{\frac{1}{3}} \text{ "=" } \frac{5 \sqrt{3}}{3}$