How do you simplify #sqrt(6250)#?

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Answer 1 · 2016-04-11T20:58:21

#sqrt(6250) = 25sqrt(10)#

First split #6250# into its prime factors:

#6250 = 2 xx 5 xx 5 xx 5 xx 5 xx 5 = 2*5^5#

We can see that the largest square number which is a factor of #6250# is:

#5^4 = (5^2)^2 = 25^2#

Hence we find:

#sqrt(6250) = sqrt(25^2*10) = sqrt(25^2)*sqrt(10) = 25sqrt(10)#

since #sqrt(ab) = sqrt(a)sqrt(b)# for any #a, b >= 0#