How do you simplify sqrt12 +sqrt 27?

Apr 26, 2016

$5 \sqrt{3}$

Explanation:

$\sqrt{12} + \sqrt{27} = \sqrt{{2}^{2} \cdot 3} + \sqrt{{3}^{2} \cdot 3} = 2 \sqrt{3} + 3 \sqrt{3} = 5 \sqrt{3}$

Note that:

• If $a \ge 0$ then $\sqrt{{a}^{2}} = a$

• If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

So if $a , b \ge 0$ then:

$\sqrt{{a}^{2} b} = \sqrt{{a}^{2}} \sqrt{b} = a \sqrt{b}$