How do you simplify #sqrt(512)#?

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Answer 1 · 2016-02-19T12:29:11

#= 2^( 9 /2)#

#sqrt(512#

We first prime factorise #512# (ie; express it as a product of its prime factors)

#512 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2#

#512 = 2^9#

#sqrt512 = sqrt(2^9)#

#= 2^( 9 xx 1/2)#

(note: square root is also called half root)

#= 2^( 9 /2)#