How do you simplify $sqrt(75)$ ?

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Answer 1 · 2016-09-11T07:26:57

$sqrt(75) = 5sqrt(3)$

First factorise $75$ :

$75 = 3*5*5$

Next note that if $a, b >= 0$ then:

$sqrt(ab) = sqrt(a)sqrt(b)$

Also if $a >= 0$ then:

$sqrt(a^2) = a$

So we find:

$sqrt(75) = sqrt(5^2*3) = sqrt(5^2)*sqrt(3) = 5sqrt(3)$

How do you simplify sqrt(75)sqrt(75) ?