Question

simplify...

$(3 + \sqrt{2} )(2 + \sqrt{2)}$
simplify...

$(3 + \sqrt{3} )(3 - \sqrt{3} )$
simplify...

$( \sqrt{5} + \sqrt{2} ) {}^{2}$
simplify..

$(\sqrt{5} - \sqrt{2} )( \sqrt{5} - \sqrt{2} )$
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Answer 1

Solution :

1. (3+√2)(2+√2)

By multiplying horizontally,

=> 3(2+√2) + √2(2+√2)

=> 6 + 3√2 + 2√2 + 2

=> 8 + 5√2

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2. (3+√3)(3-√3)

By using a² - b² = (a+b)(a-b)

=> (3)² - (√3)²

=> 9 - 3

=> 6

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3. (√5+√2)²

By using (a+b)² = a² + b² + 2ab

=> (√5)² + (√2)² + (2)(√5)(√2)

=> 5 + 2 + 2√10

=> 7 + 2√10

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4. (√5-√2)(√5-√2)

By using (a-b)² = a² + b² - 2ab

=> (√5-√2)²

=> (√5)² + (√2)² - (2)(√5)(√2)

=> 5 + 2 - 2√10

=> 7 - 2√10

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You can solve these type of questions by using Identities. It makes question easy to solve.

Answer 2

Step-by-step explanation:

$(i)(3 + \sqrt{2} )(2 + \sqrt{2} ) \\ \\ = 3(2 + \sqrt{2} ) + 2(2 + \sqrt{2} ) \\ \\ = 6 + 3 \sqrt{2} + 4 + 2 \sqrt{2} \\ \\ = 10 + 5 \sqrt{2}$

$(ii)(3 + \sqrt{ 3} )(3 - \sqrt{3} ) \\ \\ = {(3)}^{2} - {( \sqrt{3} )}^{2} \\ \\ = 9 - 3 \\ \\ = 6$

$(iii) {( \sqrt{5} + \sqrt{2}) }^{2} \\ \\ = {( \sqrt{5} )}^{2} + {( \sqrt{2}) }^{2} + 2( \sqrt{5} )( \sqrt{2} ) \\ \\ = 5 + 2 + 2 \sqrt{10} \\ \\ = 7 + 2 \sqrt{10}$

$(iv)( \sqrt{5} - \sqrt{2} )( \sqrt{5} - \sqrt{2} ) \\ \\ = {( \sqrt{5} - \sqrt{2} ) }^{2} \\ \\ = {( \sqrt{5}) }^{2} + {( \sqrt{2} )}^{2} - 2( \sqrt{5} )( \sqrt{2} ) \\ \\ = 5 + 2 - 2 \sqrt{10} \\ \\ = 7 - 2 \sqrt{10}$