Question

Rationalise the above

Answer 1

the answer is 78030 by 3

Answer 2

$\mathrm{Question : \dfrac{3}{\sqrt{5} + \sqrt{2}} + \dfrac{7}{\sqrt{5} - \sqrt{2}}}$

●  Take LCM

$\mathrm{\implies \dfrac{3\big(\sqrt{5} - \sqrt{2}\big) + 7\big(\sqrt{5} + \sqrt{2}\big) }{\big(\sqrt{5} + \sqrt{2}\big)\big(\sqrt{5} - \sqrt{2}\big) }}$

●  Use Identity : (A + B)(A - B) = A² - B²

$\mathrm{\implies \dfrac{3\sqrt{5} - 3\sqrt{2} + 7\sqrt{5} + 7\sqrt{2}}{\big(\sqrt{5}\big)^2 - \big(\sqrt{2}\big)^2}}$

●  Rearrange like terms

$\mathrm{\implies \dfrac{\big(3\sqrt{5} + 7\sqrt{5}\big) + \big(7\sqrt{2} - 3\sqrt{2}\big)}{\big(\sqrt{5}\big)^2 - \big(\sqrt{2}\big)^2}}$

$\mathrm{\implies \dfrac{10\sqrt{5} + 4\sqrt{2}}{5 - 2}}$

$\mathrm{\implies \dfrac{10\sqrt{5} + 4\sqrt{2}}{3}}$