Question

Rationalise the denominator of 3√+7+2√5
________
3√2​

Answer 1

Step-by-step explanation:

7+2

5

3

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

\begin{gathered} \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} \end{gathered}

7+2

5

3

×

7−2

5

7−2

5

=

7

2

−2

5

2

21−6

5

=

49−20

21−6

5

=

29

21−6

5

Hope it Helps

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