Question

Simplify the following expressions :
(i) (11+√11) (11-√11)(ii) (5+√7) (5-√7)
(iii) (√8 - √2) (√8 - √2)
(iv) (3+√3) (3-√3)(v) (√5 - √2) (√5 - √2)

Answer 1

Given : (i) (11 + √11) (11 - √11)  

[∵ (a + b) (a – b) = a² – b²]

⇒ (11)² - (√11)²

⇒ 121 - 11

⇒ 110

(ii) Given : (5 + √7) (5 - √7)

[∵ (a + b) (a – b) = a² – b²]

⇒ (5)² - (√7)²

⇒ 25 - 7

⇒ 18

(iii) Mistake in the question

Given : (√8 - √2) (√8 + √2)

[∵ (a + b) (a – b) = a² – b²]

⇒ (√8)² - (√2)²

⇒ 8 - 2

⇒ 6

(iv) (3 + √3) (3 - √3)

[∵ (a + b) (a – b) = a² – b²]

⇒ (3)² - (√3)²

⇒ 9 - 3

⇒ 6

(v) Mistake in the question  

Given : (√5 - √2) (√5 + √2)

[∵ (a + b) (a – b) = a² – b²]

⇒ (√5)² – (√2)²

⇒ 5 – 2

⇒ 3

HOPE THIS ANSWER WILL HELP YOU…..

Similar questions :

Simplify the following expressions :

(i) (4+√7) (3+√2)

 

(ii) (3+√3) (5 -√2)

 

(iii)(√5 -2) (√3-√5)

https://brainly.in/question/15897349

Simplify the following expression:-

(i) (5+√7)(2+√5)

(ii) (5+√5)(5-√5)

(iii) (√3+√7)^2

(iv) (√11-√7)(√11+√7)​

https://brainly.in/question/9065655

Answer 2

$\huge \fbox \red{Solution:}$

Using Identity: (a – b)(a+b) = a^2 – b^2

(i) (11 + √11) (11 – √11)

= 11^2 – (√11)^2

= 121 – 11

= 110

(ii) (5 + √7) (5 –√7 )

= (5^2 – (√7)^2 )

= 25 – 7 = 18

(iii) (√8 – √2 ) (√8 + √2 )

= (√8)^2 – (√2 ) ^2

= 8 -2

= 6

(iv) (3 + √3) (3 - √3)

= (3)^2 – (√3)^2

= 9 – 3

= 6

(v) (√5 - √2) (√5 + √2)

=(√5)^2 - (√2)^2

= 5 – 2

= 3