Question

simplify the following expression:-
(i) (5+√7)(2+√5)
(ii) (5+√5)(5-√5)
(iii) (√3+√7)^2
(iv) (√11-√7)(√11+√7)​

Answer 1

Hey there!!❤

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(1). (5 + √7)(2 + √5)

=> 5(2) + 5(√5) + √7(2) + √7(√5)

=> 10 + 5√5 + 2√7 + √35

(2). (5 + √5)(5 - √5)

=> (5)² - (√5)²

=> 25 - 5

=> 20

(3). (√3 + √7)²

=> (√3)² + (√7)² + 2(√3)(√7)

=> 3 + 7 + 2√21

=> 10 + 2√21

(4). (√11 - √7)(√11 + √7)

=> (√11)² - (√7)²

=> 11 - 7

=> 4

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Answer 2

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♦ Simplification of

(i) $(5 + \sqrt{7})(2 + \sqrt{5})$

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

$= 10 + 5 \sqrt{5} + 2 \sqrt{7} + \sqrt{ 35}$



(ii) $(5 + \sqrt{5})(5 - \sqrt{5})$

>> The above's equation is in the form of an Identity .

(a + b) (a - b)

• Let "5" be "a" and "$\sqrt{5}$" be "b" .

• Then by multiplying

$(a+b) (a-b)$

$= a^2 - ab + ab - b^2$

$= a^2 - b^2$

♦ Now by substituting value

$= 5^2 - \sqrt{5}^2$

$= 25 - 5$

$= 20$



(iii) $(\sqrt{3} + \sqrt{7} )^2$

♦ Now by using Identity

$(a+b)^2 = a^2 + 2ab + b^2$

♦ We will take

a = $\sqrt{3}$

b = $\sqrt{7}$

♦ Then

$(\sqrt{3} + \sqrt{7} )^2 = \sqrt{3}^2 + \sqrt{7}^2 + 2 \times \sqrt{3} \times \sqrt{7}$

$= 3 + 7 + 2 \sqrt{21}$

$= 10 + 2\sqrt{21}$



(iv) $(\sqrt{11} - \sqrt{7})(\sqrt{11} + \sqrt{7})$

>> The above's equation is in the form of an Identity .

(a - b) (a + b)

• Let "$\sqrt{11}$" be "a" and "$\sqrt{7}$" be "b" .

• Then by multiplying

$(a - b) (a+b)$

$= a^2 + ab - ab - b^2$

$= a^2 - b^2$

♦ Now by substituting value

$= \sqrt{11}^2 - \sqrt{7}^2$

$= 11 - 7$

$= 4$