How do you simplify $sqrt(567)$ ?

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Answer 1 · 2017-01-17T02:53:24

$sqrt567$

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 $9xx63=567$ .

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 $567$ .

$sqrt(3xx3xx3xx3xx7)$

Group like factors into pairs.

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

Rewrite each pair in exponent form.

$sqrt(3^2xx3^2xx7)$

Apply the rule $sqrt(a^2)=a$ .

$(3xx3)sqrt7$

Simplify.

$9sqrt7$

How do you simplify sqrt(567)sqrt(567)?