Question

How do you simplify `sqrt180/sqrt9`?

Answer 1

Expand your radicals

Explanation:

For positive m,n `sqrt(m*n) = sqrt(m)*sqrt(n)`.

So then we have `sqrt180 /sqrt9 = (sqrt 9 sqrt20) / sqrt9 = sqrt20 = sqrt4 sqrt5 = 2sqrt5`

Answer 2

`2sqrt5`

Explanation:

`"using the "color(blue)"laws of radicals"`

`•color(white)(x)sqrta/sqrtbhArrsqrt(a/b)`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`rArrsqrt180/sqrt9=sqrt(180/9)=sqrt20`

`rArrsqrt20=sqrt(4xx5)=sqrt4xxsqrt5=2sqrt5`