# How do you simplify sqrt675-sqrt27?

Mar 12, 2018

$12 \sqrt{3}$

#### Explanation:

$\sqrt{675} = \sqrt{225 \setminus \times 3} = 15 \sqrt{3}$
$\sqrt{27} = \sqrt{9 \setminus \times 3} = 3 \sqrt{3}$
$\sqrt{675} - \sqrt{27} = 15 \sqrt{3} - 3 \sqrt{3} = 12 \sqrt{3}$

Mar 12, 2018

sqrt(675)-sqrt(27)=color(blue)(12sqrt3

#### Explanation:

Simplify:

$\sqrt{675} - \sqrt{27}$

$\sqrt{3 \cdot {3}^{2} \cdot {5}^{2}} - \sqrt{{3}^{2} \cdot 3}$

Apply the rule: $\sqrt{{a}^{2}} = a$

$3 \cdot 5 \sqrt{3} - 3 \sqrt{3}$

Simplify.

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

Numbers that have the same square root can be added or subtracted.

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

$12 \sqrt{3}$