Question

6. Simplify by rationalizing the denominator:



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Answer 1

Answer:

2√6/(√2+√3)+6√2/(√6+√3)-8√3/(√6+√2)

=2√6(√2-√3)/(√2+√3)(√2-√3)

+6√2(√6-√3)/(√6+√3)(√6-√3)

-8√3(√6-√2)/(√6+√2)(√6-√2)

=2√6(√2-√3)/(√2^2-√3^2)+6√2(√6-√3)/(√6^2-√3^2)-8√3(√6-√2)/(√6^2-√2^2)

=2√6(√2-√3)/(2-3)+6√2(√6-√3)/(6-3)

-8√3(√6-√2)/(6-2)

=2√6(√2-√3)/-1+6√2(√6-√3)/3-8√3(√6-√2)/4

=2√6(√3-√2)+2√2(√6-√3)-2√3(√6-√2)

=2√18-2√12+2√12-2√6-2√18+2√6

=0