Question : Which of the following is the correct-rationalised form of $\frac{15}{\sqrt5+2}$?
Option 1: $5\sqrt5-6$
Option 2: $5\sqrt5-30$
Option 3: $15\sqrt5-30$
Option 4: $45\sqrt5-30$
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Correct Answer: $15\sqrt5-30$
Solution : Given: $\frac{15}{\sqrt{5}+2}$ Now rationalising with $\sqrt{5}-2$, we get, $\frac{15}{\sqrt{5}+2}\times\frac{\sqrt{5}-2}{\sqrt{5}-2}$ $= \frac{15(\sqrt{5}-2)}{(\sqrt{5})^{2}-2^{2}}$ $= \frac{15(\sqrt{5}-2)}{5-4}$ $= \frac{15(\sqrt{5}-2)}{1}$ $= 15\sqrt{5}-30$ Hence, the correct answer is $15\sqrt{5}-30$.
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