Question

pls rationalise the denominator​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{\dfrac{7\sqrt{3}-5\sqrt{2}}{\sqrt{48}+\sqrt{18}}}$

$\sf{=\dfrac{7\sqrt{3}-5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}}$

$\sf{=\dfrac{(7\sqrt{3}-5\sqrt{2})(4\sqrt{3}-3\sqrt{2})}{(4\sqrt{3}+3\sqrt{2})(4\sqrt{3}-3\sqrt{2})}}$

$\sf{=\dfrac{(7\sqrt{3}-5\sqrt{2})(4\sqrt{3}-3\sqrt{2})}{(4\sqrt{3})^2-(3\sqrt{2})^2}}$

$\sf{=\dfrac{7\sqrt{3}\cdot4\sqrt{3}-5\sqrt{2}\cdot4\sqrt{3}-3\sqrt{2}\cdot7\sqrt{3}+3\sqrt{2}\cdot5\sqrt{2}}{(4\sqrt{3})^2-(3\sqrt{2})^2}}$

$\sf{=\dfrac{84-20\sqrt{6}-21\sqrt{6}+30}{(4\sqrt{3})^2-(3\sqrt{2})^2}}$

$\sf{=\dfrac{114-41\sqrt{6}}{48-18}}$

$\sf{=\dfrac{114-41\sqrt{6}}{30}}$