How do you simplify $\sqrt{75}$ $sqrt(75)$ ?

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Answer 1 · 2016-09-11T07:26:57

$\sqrt{75} = 5 \sqrt{3}$ $sqrt(75) = 5sqrt(3)$

First factorise $75$ $75$ :

$75 = 3 \cdot 5 \cdot 5$ $75 = 3*5*5$

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

$\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$

Also if $a \geq 0$ $a >= 0$ then:

$\sqrt{a^{2}} = a$ $sqrt(a^2) = a$

So we find:

$\sqrt{75} = \sqrt{5^{2} \cdot 3} = \sqrt{5^{2}} \cdot \sqrt{3} = 5 \sqrt{3}$ $sqrt(75) = sqrt(5^2*3) = sqrt(5^2)*sqrt(3) = 5sqrt(3)$

How do you simplify √75sqrt(75) ?