Question

5√2+3√3+5√3-2√2 answer in steps​

Answer 1

Step-by-step explanation:

Answer:

\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}=\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19}

Step-by-step explanation:

Consider,

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

We multiply and divide by 2√2 - 3√3

we get,

\implies\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}\times\frac{2\sqrt{2}-3\sqrt{3}}{2\sqrt{2}-3\sqrt{3}}

\implies\frac{(2\sqrt{3}-\sqrt{5})(2\sqrt{2}-3\sqrt{3})}{(2\sqrt{2}+3\sqrt{3})(2\sqrt{2}-3\sqrt{3})}

\implies\frac{4\sqrt{6}-6\times3-2\sqrt{10}+3\sqrt{15}}{(2\sqrt{2})^2-(3\sqrt{3})^2}

\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{8-27}

\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{-19}

\implies\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19}

4.1

Answer 2

5√2-2√2+3√3+5√3

=3√2 + 8√3