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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: $45\sqrt5-30$


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

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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