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 $a, b >= 0$

How do you simplify sqrt(6250)sqrt(6250)?