Question

rationalise the denominators:-
1. 1/√5+√2
2. 1/√7-2

Answer 1

1)1/5^1/2+2^1/2=(1*5^1/2-2^1/2)/(5^1/2+2^1/2)(5^1/2-2^1/2)
                           =(5^1/2-2^1/2)/5-4
                           =5^1/2-2^1/2
2)1/7^(1/2)-2=(1*7^1/2+2)/(7^1/2-2)(7^1/2+2)
                     =(7^1/2+2)/7-4
                     =(7^1/2+2)/3

Answer 2

1/√5  +√22/√7-2

1/√5=1/√5×√5/√5=√5/5

√22/√7-2==√22/√7-2×√7+2/√7+2==√22[√7+2]/7-4==√154+2√22/3

1/√5+√22/√7-2==√5/5+√154+2√22/3==3√5+5√154+10√22/15

hence denominator rationalised