Question

Rationalize the denominator.

$\huge \tt \frac{3}{ 2\sqrt{5} - 3 \sqrt{2}}$

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Answer 1

$\dfrac{6 \sqrt{5} + 9 \sqrt{2} }{2}$

Step-by-step explanation:

$\displaystyle{\frac{3}{ 2\sqrt{5} - 3 \sqrt{2}}}$

$= \dfrac{3}{ 2\sqrt{5} - 3 \sqrt{2}}\times \dfrac{2\sqrt{5} + 3 \sqrt{2}}{2\sqrt{5} + 3 \sqrt{2}}$

$= \dfrac{3(2 \sqrt{5} + 3 \sqrt{2} )}{(2 \sqrt{5} - 3 \sqrt{2})(2 \sqrt{5} + 3 \sqrt{2})}$

$= \dfrac{6 \sqrt{5} + 9 \sqrt{2} }{(2 \sqrt{5} ) ^{2} - (3 \sqrt{2}) ^{2} } \qquad \sf\purple{[ {(a + b)(a - b) = {a}^{2} - {b}^{2} }]}$

$= \dfrac{6 \sqrt{5} + 9 \sqrt{2} }{20 - 18}$

$= \dfrac{6 \sqrt{5} + 9 \sqrt{2} }{2}$

$\green{\underline{\pink{\boxed{\blue{\bf{\therefore \dfrac{3}{ 2\sqrt{5} - 3 \sqrt{2}} = \dfrac{6 \sqrt{5} + 9 \sqrt{2} }{2} }}}}}}$

Concepts Used :-

1. Some algebraic identities

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b) (a - b) = a² - b²

2. Multiply both numerator as well as denominator by conjugate pair.

Answer 2

Answer:

refer to the above attachment