# How do you evaluate \sqrt { \frac { 27} { 9} } + 5?

Dec 14, 2017

$\sqrt{3} + 5$

= 6.73205

#### Explanation:

The expression can be rewritten as:

${\left({3}^{3} / {3}^{2}\right)}^{\frac{1}{2}}$ + 5

and thus, applying the exponent outside the bracket:

$\left({3}^{\frac{3}{2}} / 3\right) + 5$

= $\left(\frac{3 \sqrt{3}}{3}\right) + 5$

= $\sqrt{3} + 5$

= 6.73205

Dec 14, 2017

$6.7321$

#### Explanation:

$\sqrt{\frac{27}{9}} + 5$

$\frac{\sqrt{27}}{3} + 5$

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

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

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

$\frac{3 \sqrt{3}}{3} + 5$

$\frac{\cancel{3} \sqrt{3}}{\cancel{3}} + 5$

$\sqrt{3} + 5$

$1.7321 + 5$

$6.7321$

Dec 14, 2017

$= \sqrt{3} + 5$

$= 6.732$

#### Explanation:

Simplify under the root first:

$\sqrt{\frac{27}{9}} + 5$

$= \sqrt{\frac{\cancel{9} \times 3}{\cancel{9}}} + 5$

$= \sqrt{3} + 5$

$\sqrt{3}$ is an irrational number, so you have to round off if you calculate the answer as a decimal.

$= 1.732 + 5$

$= 6.732$