Question

How do you simplify `sqrt((2g^3)/(5z))`?

Answer 1

`(sqrt(10gz)*g)/(5z)`

Explanation:

First, begin by "distributing" the square root sign to the numerator and denominator:
`sqrt(2g^3)/(sqrt(5z)`
Now simplify the top:
`(sqrt(2)sqrt(g^3))/sqrt(5z)` (because `sqrt(ab) = sqrt(a)sqrt(b)`)

`(sqrt(2)*gsqrt(g))/sqrt(5z)` (for example, `sqrt(2^3) = sqrt(8) = 2sqrt(2)`)

Since it isn't proper to have a square root in the denominator, we take it out by multiplying by `sqrt(5z)/sqrt(5z)`.

`(sqrt(2)*gsqrt(g))/sqrt(5z)*sqrt(5z)/sqrt(5z)`

`(sqrt(2)*gsqrt(g)*sqrt(5z))/(5z)` (`sqrt(5z)*sqrt(5z) = 5z`)

We can now finally collect all of our radicals (square roots) into one neat sign:

`(sqrt(10zg)*g)/(5z)` (remember that `sqrt(a)sqrt(b)sqrt(c) = sqrt(abc)`)

And that is the final answer.