Question

Simplify each of the following by rationalising the denominator:
3 root5-root7/3 root3+root 2

Answer 1

hop it helps Mark as brainliest

Answer 2

Answer:

After simplification we get, $=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}$

Step-by-step explanation:

Given Expression:

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

We need to simplify the given expression by rationalizing the denominator.

Consider,

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

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

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

$=\frac{9\sqrt{5}\sqrt{3}-3\sqrt{5}\sqrt{2}-3\sqrt{7}\sqrt{3}+\sqrt{7}\sqrt{2}}{(3\sqrt{3})^2-(\sqrt{2})^2}$

$=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{3^2\times3-2}$

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

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

Therefore, After simplification we get, $=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}$