# How do you simplify Square root of 63 - Square root of 28?

##### 2 Answers
Mar 3, 2018

$\setminus \sqrt{63} - \setminus \sqrt{28} = \setminus \sqrt{{3}^{2} \cdot 7} - \setminus \sqrt{{2}^{2} \cdot 7} = 3 \setminus \sqrt{7} - 2 \setminus \sqrt{7} = \setminus \sqrt{7}$

Mar 3, 2018

$\sqrt{7}$

#### Explanation:

We must use our surd knowledge:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$\implies \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3 \sqrt{7}$

$\implies \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2 \sqrt{7}$

$\therefore \sqrt{63} - \sqrt{28} \equiv 3 \sqrt{7} - 2 \sqrt{7}$

$= \sqrt{7}$