# How do you simplify sqrt(567)?

Jan 17, 2017

$\sqrt{567}$

The numbers 5, 6, and 7 equal 18. So it is divisible by 9.

I divided 567 by 9, and found the quotient equal to 63.

So $9 \times 63 = 567$.

So, the prime factors of 9 are 3 and 3, and the prime factors for 63 are 7 and 9.

List the prime factors for $567$.

$\sqrt{3 \times 3 \times 3 \times 3 \times 7}$

Group like factors into pairs.

sqrt((3xx3)xx(3xx3)xx7))

Rewrite each pair in exponent form.

$\sqrt{{3}^{2} \times {3}^{2} \times 7}$

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

$\left(3 \times 3\right) \sqrt{7}$

Simplify.

$9 \sqrt{7}$