# How do you simplify sqrt175-sqrt27+sqrt28?

May 15, 2016

$\text{ } 7 \sqrt{7} - 3 \sqrt{3}$

#### Explanation:

If you can not easily spot the common factors etc try investigation with factor trees.

Write as

$\text{ } \textcolor{b r o w n}{\sqrt{175} - \sqrt{27} + \sqrt{28}} \textcolor{b l u e}{\to \sqrt{{5}^{2} \times 7} - \sqrt{{3}^{3} \times 3} + \sqrt{{2}^{2} \times 7}}$

$\text{ } 5 \sqrt{7} - 3 \sqrt{3} + 2 \sqrt{7}$

$\text{ } 7 \sqrt{7} - 3 \sqrt{3}$