Question

Q.Simplify each of the following by rationalising the denominator
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Answer 1

$\sf \rightarrow \quad \dfrac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \\ \\ \sf \rightarrow \quad \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \\ \sf \rightarrow \quad \frac{ {(7 + 3 \sqrt{5} )}^{2} }{ {(7)}^{2} - {(3 \sqrt{5} )}^{2} } \qquad \bigg( \: \because \: (a + b)(a - b) = {a}^{2} - {b}^{2} \: \bigg) \\ \\ \sf \rightarrow \quad \frac{ {(7)}^{2} + {(3 \sqrt{5}) }^{2} + 2 \cdot 7 \cdot 3 \sqrt{5} }{49 - 45} \\ \\ \sf \rightarrow \quad \frac{ 49 + 45 + 42 \sqrt{5} }{4} \\ \\ \sf \rightarrow \quad \frac{94 + 42 \sqrt{5} }{4} \\ \\ \sf \rightarrow \quad \frac{\cancel{2}^{1}(47 + 21\sqrt{5}) }{\cancel{4}_{2}} \\ \\ \sf \Rightarrow \quad \frac{ 47 + 21\sqrt{5} }{2}$

Answer 2

ANSWER:-

Explanation:

Explanation:(7+3√5)(7-3√5)

3√5)

3√5) (a+b)(a-b)=a2−b2

2

(7+3√5)(7−3√5)=72-(3√5)2

(3√5)2

(3√5)2 =49−32√52

2

2 =49−9×5

2 =49−9×5 =49−45

2 =49−9×5 =49−45 =4

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