How do you simplify $sqrt(72)$ ?

Question

2172 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-01T12:39:25

$sqrt72 = 6sqrt2$

Check to see if $72$ is divisible by a perfect square:
$2^2 = 4$ and $72 = 4*18$
So $sqrt72 = sqrt(4*18) = sqrt4*sqrt18 =2sqrt18$

Continue be checking to see is $18$ is divisible by a perfect square:
$2^2 = 4$ , and $18$ is not divisible by $4$
$3^2=9$ and $18=9*2$

so we get:
$sqrt72 = 2sqrt18 = 2sqrt(9*2)=2sqrt9sqrt2=2*3sqrt3=6sqrt2$

There are many ways of writing/working this simplification. Here are a few more:

$sqrt72 = sqrt(4*9*2) = 2*3*sqrt2 = 6sqrt2$

$sqrt72 = sqrt (36*2) = sqrt36sqrt2=6sqrt2$

$sqrt72 = sqrt(2^3*3^2) = sqrt(2^2*2*3^2) = 2*sqrt2*3 = 6sqrt2$

How do you simplify sqrt(72)sqrt(72)?