Question

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

Answer 1

`=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`