Question

How do you simplify the square root of 27a?

Answer 1

Remember
$\sqrt{ab}=(\sqrt{a})(\sqrt{b})$

so

$\sqrt{27a}=(\sqrt{27})(\sqrt{a})=$
$(\sqrt{(3)(3)(3)})(\sqrt{a})=$
$(\sqrt{(3)(3)})(\sqrt{3})(\sqrt{a}=$
$(3)(\sqrt{3})(\sqrt{a})=$
$(3)(\sqrt{3a})=$
$3\sqrt{3a}$

Answer 2

You split a square root into two square roots if it is not a prime number.

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

Find two factors where one is a perfect square.

$\sqrt{27a} = \sqrt{3a}\sqrt{9} = 3\sqrt{3a}$