Question

3√7/√5+√2-5√5/√2+√7+2√2/√7+√5 Simplify

Answer 1

Step-by-step explanation:

Given : Expression \frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}

To find : Simplify the given number by rationalizing the denominator?

Solution :

\frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}

Rationalizing the denominator by multiplying and dividing denominator by opposite sign,

=\frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}\times\frac{3\sqrt{3}-\sqrt{2}}{3\sqrt{3}-\sqrt{2}}

=\frac{(3\sqrt{5}-\sqrt{7})(3\sqrt{3}-\sqrt{2})}{(3\sqrt{3})^2-(\sqrt{2})^2}

=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{27-2}

=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}