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#