Question

Q: Rationalise the denominator 3/7+2√5​

Answer 1

$\frac{3}{7 + 2 \sqrt{5} }$

To make the Denominator Rational, we need to make the √5 Rational.

We Know, a² - b² = (a+b)(a-b)

So,

Multiplying Both the Numerator and Denominator by 7 - 2√5. We get

$\frac{3}{7 + 2 \sqrt{5} } \times \frac{7 - 2 \sqrt{5} }{7 - 2 \sqrt{5} } \\ = \frac{21 - 6 \sqrt{5} }{ {7}^{2} - {2 \sqrt{5} }^{2} } \\ = \frac{21 - 6 \sqrt{5} }{49 - 20} \\ = \frac{21 - 6 \sqrt{5} }{29}$

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Answer 2

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