Simplify the square root of a fraction

Question

I am supposed to simplify √(48/147). The answer is 4/7, but I'm not sure why. It seems like this would be the same as  (√48)/(√147), but that answer does not seem to be 4/7. Can you please show me the steps to get this answer? Thanks so much!

Answer 1

Elizabeth

 

48 is the product of 16 * 3 and the square root of 16 is 4 so the numerator is really 4 radical 3

 

147 is the product of 49 and 3 and the square root of 49 is 7 so the denominator is really 7 radical 3

 

The radical 3s cancel out and you are left with 4/7

 

All the best

 

Lori