Question

Evaluate: 8√3/√10+√3 - 4√5/√6+√5 - 7√2/√15+3√2​

Answer 1

Answer:

ARoy Expert

√(5+2√6)

=√(3+2+2√3.√2)

=√{(√3)²+2.√3.√2+(√2)²}

=√(√3+√2)²

=√3+√2  (neglecting the negative sign)

√(8-2√15)

=√(5+3-2.√5.√3)

=√{(√5)²-2.√5.√3+(√3)²}

=√(√5-√3)²

=√5-√3 (neglecting the negative sign)

∴, √(5+2√6)+√(8-2√15)

=√3+√2+√5-√3

=√2+√5 Ans.

Read more on Brainly.in - https://brainly.in/question/746370#readmore

Answer 2

$\frac{8\sqrt{3} }{\sqrt{10}+\sqrt{3} } -\frac{4\sqrt{5} }{\sqrt{6}+\sqrt{5} } -\frac{7\sqrt{2} }{\sqrt{15}+\sqrt{2} }$

Rationalising the denominator,

= $\frac{8\sqrt{3}(\sqrt{10}-\sqrt{3})}{7} -4\sqrt{5} (\sqrt{6} -\sqrt{5} )+\frac{7\sqrt{2}(\sqrt{15}-3\sqrt{2}) }{3}$

= $\frac{8\sqrt{30} }{7} -\frac{24}{7} -4\sqrt{30}-20+\frac{7\sqrt{30} }{3}-14$

=$\frac{-11\sqrt{30} }{21} -\frac{214}{7}$