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

1 Answer
Don't Memorise
Sep 24, 2015

#=color(blue)(5/6#

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#

#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#

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