How would I solve this radical?

Question

6√120÷√15

 

Answer 1

Okay, this one can be managed a few slightly different ways, but they all lead in the same direction. Let's take the path you will find easiest to follow:

First, since both roots have the same index (i.e., it's not an awkward mix of a cube root and a square root), we can place them under one radical:

6 √(120 / 15)

Now, we reduce:

6 √8

We ask if 8 breaks into any numbers with a perfect root. In this case, yes! 4*2:

6√(4*2)

6√4 * √2

6*2√2

12√2

 

 

Answer 2

6√120/√15 = 6√8 = 6√4√2 = 6(2)√2 = 12√2