How do you simplify sqrt(500/720)√500720?

1 Answer
Don't Memorise
Sep 24, 2015

=color(blue)(5/6=56

Explanation:

We first simplify both terms individually by prime factorisation:

sqrt(500) = sqrt(5*5*5*2*2) = sqrt(5^2 *5 *2^2) = 5 *2 sqrt5 =10sqrt5√500=√5⋅5⋅5⋅2⋅2=√52⋅5⋅22=5⋅2√5=10√5

sqrt(720) = sqrt(3^2 * 2^2 * 2 ^2*5) = 3*2*2sqrt5=12sqrt5√720=√32⋅22⋅22⋅5=3⋅2⋅2√5=12√5

Now our expression becomes:
(10sqrt5)/(12sqrt5)=(10cancelsqrt5)/(12cancelsqrt5)

=10/12

=color(blue)(5/6

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