Question

How do you rationalize the denominator and simplify `sqrt24/sqrt3`?

Answer 1

`sqrt(24)/sqrt(3) = 2sqrt(2)`

Explanation:

We will use:

• If `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`

• If `b > 0` then `sqrt(a/b) = sqrt(a)/sqrt(b)`

The normal way to solve this example is to multiply both the numerator and denominator by `sqrt(3)` first:

`sqrt(24)/sqrt(3) = (sqrt(24)*sqrt(3))/(sqrt(3)*sqrt(3)) = sqrt(72)/3 = sqrt(6^2*2)/3 = (sqrt(6^2)*sqrt(2))/3 = (6sqrt(2))/3 = 2sqrt(2)`

Alternatively, we can combine the numerator and denominator inside the square root:

`sqrt(24)/sqrt(3) = sqrt(24/3) = sqrt(8) = sqrt(2^2)*sqrt(2) = 2sqrt(2)`