Question

Simplify 7 root 3 by root 3 + root 3 minus 2 root 5 by 6 root + root 5 minus 3 root 2 by root 15 + 3 root 2

Answer 1

Answer:

Step-by-step explanation:

Step-by-step explanation:

The given equation is :

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

Rationalizing this equation, we get

=\frac{7\sqrt{3}(\sqrt{10}-\sqrt{3})}{10-3}-\frac{2\sqrt{5}(\sqrt{6}-\sqrt{5})}{6-5}-\frac{3\sqrt{2}(\sqrt{15}-3\sqrt{2})}{15-18}

=\sqrt{3}(\sqrt{10}-\sqrt{3})-2\sqrt{5}(\sqrt{6}-\sqrt{5})+\sqrt{2}(\sqrt{15}-3\sqrt{2})

=\sqrt{30}-3-2\sqrt{30}+10+\sqrt{30}-6

=1