Question

Plz answer this question with correct explanation​

Answer 1

Answer:

simplify and express the result in its simplest form 3√2×√5

Answer 2

Answer:

$\frac{22}{2+\sqrt{3}+\sqrt{5}}=4-2\sqrt{15}+\sqrt{5}+3\sqrt{3}$

Step-by-step explanation:

$\bold{Given: \frac{22}{2+\sqrt{3}+\sqrt{5}} }$

We have to rationalize the denominator.

$\frac{22}{(2+\sqrt{2})+\sqrt{5}}$

$\implies\frac{22}{(2+\sqrt{3})+\sqrt{5}}\times\frac{(2+\sqrt{3})-\sqrt{5}}{(2+\sqrt{3})-\sqrt{5}}$

$\implies\frac{22(2+\sqrt{3}-\sqrt{5})}{((2+\sqrt{3})-\sqrt{5})((2+\sqrt{3})-\sqrt{5})}$

$\implies\frac{22(2+\sqrt{3}-\sqrt{5})}{((2+\sqrt{3})-\sqrt{5})((2+\sqrt{3})-\sqrt{5})}$

$\implies\frac{22(2+\sqrt{3}-\sqrt{5})}{(2+\sqrt{3})^2-(\sqrt{5})^2}$

$\implies\frac{44+22\sqrt{3}-22\sqrt{5}}{4+(\sqrt{3})^2+4\sqrt{3}-5}$

$\implies\frac{44+22\sqrt{3}-22\sqrt{5}}{2+4\sqrt{3}}$

$\implies\frac{22+11\sqrt{3}-11\sqrt{5}}{1+2\sqrt{3}}$

$\implies\frac{22+11\sqrt{3}-11\sqrt{5}}{1+2\sqrt{3}}\times\frac{1-2\sqrt{3}}{1-2\sqrt{3}}$

$\implies\frac{(22+11\sqrt{3}-11\sqrt{5})(1-2\sqrt{3})}{(1+2\sqrt{3})(1-2\sqrt{3})}$

$\implies\frac{22\sqrt{15}-11\sqrt{5}-33\sqrt{3}-44}{1-(2\sqrt{3})^2}$

$\implies\frac{22\sqrt{15}-11\sqrt{5}-33\sqrt{3}-44}{-11}$

$\implies4-2\sqrt{15}+\sqrt{5}+3\sqrt{3}$

$\bold{Therefore, \frac{22}{2+\sqrt{3}+\sqrt{5}}=4-2\sqrt{15}+\sqrt{5}+3\sqrt{3} }$