Question

rationalise the denomenator of 12 by 3+√5-2√2

Answer 1

refer the attachment

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Answer 2

Answer:

Given

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

Rationalize the denominator

Solution

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

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

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

or a² - b² = ( a + b ) ( a - b )

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

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

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

$17 - 12 \sqrt{2}$

Note :

Some important identities

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