# How do you simplify sqrt(972)?

Apr 24, 2016

$18 \sqrt{3}$

#### Explanation:

972 ends in 2, therefore is divisible by 2:

$\frac{972}{2} = 486$

divisible by 2 again:

$\frac{486}{2} = 243$

The sum of digits is multiple of 3, so 243 it is divisble by 3:

$\frac{243}{3} = 81$

$81 = 9 \times 9 = {3}^{4}$

so $972 = {2}^{2} \times {3}^{5}$

$\sqrt{972} = \sqrt{{2}^{2} \times {3}^{5}} = \sqrt{{2}^{2} \times {3}^{4} \times 3} = 2 \times {3}^{2} \sqrt{3} = 18 \sqrt{3}$