How do you simplify $sqrt(500/720)$ ?

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Answer 1 · 2015-09-24T08:12:07

$=color(blue)(5/6$

We first simplify both terms individually by prime factorisation:

$sqrt(500) = sqrt(5*5*5*2*2) = sqrt(5^2 *5 *2^2) = 5 *2 sqrt5 =10sqrt5$

$sqrt(720) = sqrt(3^2 * 2^2 * 2 ^2*5) = 3*2*2sqrt5=12sqrt5$

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

$=10/12$

$=color(blue)(5/6$

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