# Please solve this? question in the attachment

##### 2 Answers
May 10, 2018

$= \frac{203}{9} \sqrt{3}$

#### Explanation:

We will use the fact that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$7 \cdot \frac{\sqrt{1}}{\sqrt{3}} - \frac{7}{3} \cdot \frac{\sqrt{1}}{\sqrt{3}} + 3 \sqrt{147}$

$= \frac{7}{\sqrt{3}} - \frac{7}{3 \sqrt{3}} + 3 \sqrt{147}$

$= \frac{7 \sqrt{3}}{3} - \frac{7 \sqrt{3}}{9} + 3 \sqrt{147}$

$= \frac{21 \sqrt{3}}{9} - \frac{7 \sqrt{3}}{9} + 3 \sqrt{147}$

$= \frac{14 \sqrt{3}}{9} + 3 \sqrt{147}$

I've left the $3 \sqrt{147}$ up till now, cos its nasty to deal with. However, seeing that we have an expression with $\sqrt{3}$, there's a good chance that 147 will be equal to three times a square number. Some good ol' bus shelter long division (or using a calculator if you're allowed) will show you that $147 = 3 \times 49$ Since 49 is a square number, we can work on simplifying this more

$= \frac{14 \sqrt{3}}{9} + 3 \left[\sqrt{3 \times 49}\right]$

$= \frac{14 \sqrt{3}}{9} + 3 \left(7 \sqrt{3}\right)$

$= \frac{14 \sqrt{3}}{9} + 21 \sqrt{3}$

$= \frac{14 \sqrt{3}}{9} + \frac{189 \sqrt{3}}{9}$

$= \frac{203}{9} \sqrt{3}$

May 10, 2018

=39.06736822

#### Explanation:

$\sqrt{\frac{1}{3}} = \frac{\sqrt{3}}{3}$

$\sqrt{147} = \sqrt{49} \times \sqrt{3} = 7 \sqrt{3}$

$7 \sqrt{\frac{1}{3}} - 2 \frac{1}{3} \sqrt{\frac{1}{3}} + 3 \sqrt{147}$

=$\frac{7 \sqrt{3}}{3} - \frac{7 \sqrt{3}}{9} + 21 \sqrt{3}$

$\frac{14 \sqrt{3}}{9} + 21 \sqrt{3} = \frac{203 \sqrt{3}}{9}$

=39.06736822