Given: 1/[(8√11) - (7√5)]
It is known that the conjugate of (8√11) - (7√5) is (8√11) + (7√5)
To rationalize the denominator of the given fraction, multiply the conjugate of denominator on both numerator and denominator.
= [1/[(8√11) - (7√5)]] × [[(8√11) + (7√5)]/[(8√11) + (7√5)]]
= [(8√11) + (7√5)]/[(8√11)2- (7√5)2]
= [(8√11) + (7√5)]/[704- 245]
= [(8√11) + (7√5)]/459