Question

rationalise the denomenator of 3-2√2/3+2√2
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Answer 1

$\huge\underline\mathtt{Given}$

$\sf \frac{3-2\sqrt{2}}{3+2\sqrt{2}}$

Rationalize the denominator

$\huge\underline\mathtt{Solution}$

$\implies\sf \Large\frac{3-2\sqrt{2}}{3+2\sqrt{2}}$

$\implies\sf \Large\frac{3-2\sqrt{2}}{3+2\sqrt{2}}\times\frac{3-2\sqrt{2}}{3-2\sqrt{2}}$

Applying both identity (a-b)² = a²+b²-2ab

or a²- b² = (a+b)(a-b)

$\implies\sf \Large\frac{(3-2\sqrt{2})^{2}}{(3)^2-(2\sqrt{2})^{2}}$

$\implies\sf \Large\frac{(3)^2+(2\sqrt{2})^{2}-2\times{3}\times{2\sqrt{2}}}{9-8}$

$\implies\sf \Large\frac{9+8-12\sqrt{2}}{1}$

$\implies\sf 17-12\sqrt{2}$

Note :

Some important identities

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• a²-b² = (a+b)(a-b)
• (a+b)³ = a³+b³+3ab(a+b)
• (a-b)³ = a³-b³-3ab(a-b)
• a³-b³ = (a-b)(a²+ab+b²)
• a³+b³ = (a+b)(a²-ab+b²)

Answer 2

Answer:

17 - 12√2

Step by step explanation:

To do:

Rationalise the denomenator

Solution:

$\frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \frac{(3 - 2 \sqrt{2} )(3 - 2\sqrt{2}) }{(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2}) }$

I multiply the denominator by the conjugate surds to make it rational.

$\frac{ {(3 - 2 \sqrt{2}) }^{2} }{ {(3)}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ \frac{ {(3)}^{2} + (2 { \sqrt{2}) }^{2} - 2.3.2 \sqrt{2} }{9 - 8} \\ \\ \frac{9 + 8 - 12 \sqrt{2} }{1} \\ \\ 17 - 12 \sqrt{2}$

Hence, the required answer is 17 - 12√2 .

Formula Used

(a - b)² = a² + b² - 2ab

(a² - b²) = (a - b)(a + b)