Question

rationalise the denominator 1 /

Answer 1

1/(√7+√6)-(√13)
Now the denominator is in the form of a-b and the conjugate of a-b is a+b

1 (√7+√6)+(√13)÷{(√7+√6)-(√13)}{(√7+√6)-(√13)}

=(√7+√6+√13) ÷ (√7+√6)^2-(√13)^2
[ as (a+b)(a-b ) = a^2 -b^2]
=( √7+√6+√13 )÷( 7+6 +2√42)- 13
= ( √7+√6+√13 ) ÷ 13 -13 +2√42
= ( √7+√6+√13 ) /(2√42)

Again by rationalizing the denominator

=( √7+√6+√13 ) /( 2√42)
=( √7+√6+√13 ) ( √42)/ ( 2√42)( √42)
= (7√6+6√7+√546)/ 84