Question

Simplify 8√27 (show work)

Answer 1

I was taught that if you must simplify a square root by doing the birthday cake method. Basically divide the radical by its lowest common factor until it can't be divided anymore. Also the lowest factor can't be 1. For 27, the lower common factor is 3.

27/3 = 9/3 = 3

Since in a common square root the index is 2, you must pair the least common factors. There is 1 pair of 3 and there is 1 remaining

$\sqrt{27}$ is 3$\sqrt{3}$.

You must multiply 3 and 8, which gives 24

The answer is 24$\sqrt{3}$