rationalise the denominator?

Question

1) √12
√48
2)√5
√80
3) √12
√156
4) √7
√63
(The top surd divide by the bottom one)
I know how to rationalise the denominator of simple surds but these are the difficult ones.
Could someone please help and explain how they got to the final answer.
Thank you

Answer 1

1) √12/√48 = √(12/48) =√(1/4)=1/2
2) √5/√80 = √(5/80) = √(1/16) = 1/4
3) √12/√156 = √(1/13)= √13/13
4) √(7/63) =√(1/9) 1/3

Answer 2

1) √12 / √48 = 1/√4 = 1/2 or -1/2

2)√5 / √80 = 1 / √16 = 1/4 or -1/4
3) √12 / √156 = 1 / √13
4) √7 / √63 = 1 / √9 = 1/3 or -1/3

The procedure is simple. Find the fractions of the denominator and id the numerator and denominator are common, cancel them out and see whether the balance root is an integer.

Answer 3

This will help you... √(ab)=√a√b

1) √12/√48 = √12/(√12√4)=1/2 after cancelling the √12 and dealing with √4=2.

2)√5/√80 = √5/(√5√16)= 1/4 after cancelling √5...

Can you figure it out from here? Factor the denominators.

3) √12/√156

4) √7/√63