# Question 1eeb2

Mar 1, 2017

$2 \sqrt{3}$

#### Explanation:

In this format the brackets do not do anything so disregard them.

$\frac{15}{\sqrt{3}} - \sqrt{27}$

Mathematicians do not like roots in the denominator so lets 'get rid' of it. Multiply by 1 and you do not change a value. However, 1 comes in many forms so you can change the way something looks without changing its intrinsic value.

color(green)([15/sqrt(3)color(red)(xx1)]-sqrt(27)

color(green)([15/sqrt(3)color(red)(xxsqrt(3)/sqrt(3))]-sqrt(27)#

$\textcolor{g r e e n}{\left[\frac{15 \sqrt{3}}{3}\right] - \sqrt{27}}$

But $\sqrt{27} = \sqrt{3 \times 9} = \sqrt{3 \times {3}^{2}} = 3 \sqrt{3}$

$\frac{15 \sqrt{3}}{3} - 3 \sqrt{3}$

Factor out the $\sqrt{3}$

$\sqrt{3} \times \left[\frac{15}{3} - 3\right]$

$\sqrt{3} \times \frac{6}{3}$

$2 \sqrt{3}$