$\dfrac{5}{\sqrt{7} + \sqrt{2}}$ has rationalised value

$\dfrac{5}{\sqrt{7} + \sqrt{2}}$ has rationalised value
  1. $\sqrt{7} - \sqrt{2}$
  2. $\sqrt{7} + \sqrt{2}$
  3. $\dfrac{\sqrt{7} - \sqrt{2}}{5}$
  4. $\dfrac{5}{5}$

Solution

Multiply by $\dfrac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$. Denom $= 7 - 2 = 5$. Numerator $= 5(\sqrt{7} - \sqrt{2})$. Result: $\sqrt{7} - \sqrt{2}$.

Asked in: MH-SSC-9

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