Question

Evaluate: (7√3 / √10 + √3)- (3√2 / √15 + 3√2) (2√5 / √6 + √5)

Answer 1

7√3/(√10+√3)-3√2/(√15+3√2)-2√5/(√6+√5)
={7√3(√10-√3)/(√10+√3)(√10-√3)}-3√2(√15-3√2)/(√15+3√2)(√15-3√2)-
2√5(√6-√5)/(√6+√5)(√6-√5)
={7√3(√10-√3)/(10-3)}-3√2(√15-3√2)/(15-18)-2√5(√6-√5)/(6-5)
=√3(√10-√3)+√2(√15-3√2)-2√5(√6-√5)
=√30-3+√30-6-2√30+10
=10-9
=1

Answer 2

7√3/(√10+√3)-3√2/(√15+3√2)-2√5/(√6+√5)

={7√3(√10-√3)/(√10+√3)(√10-√3)}-3√2(√15-3√2)/(√15+3√2)(√15-3√2)-

2√5(√6-√5)/(√6+√5)(√6-√5)

={7√3(√10-√3)/(10-3)}-3√2(√15-3√2)/(15-18)-2√5(√6-√5)/(6-5)

=√3(√10-√3)+√2(√15-3√2)-2√5(√6-√5)

=√30-3+√30-6-2√30+10

=10-9

=1