Question

"Question 2 Simplify each of the following expressions:
(i) (3 + 3^(1/2)(2 + 2^(1/2)
(ii) (3 + 3^(1/2)((3 - 3^(1/2)
(iii) [5^(1/2) + 2^(1/2)]^2
(iv)[5^(1/2) + 2^(1/2)][5^(1/2) - 2^(1/2)]

Class 9 - Math - Number Systems Page 24"

Answer 1

hope it helps u... Mark my answer as brainliest :)

Answer 2

Here we simplify these expressions by using the identities.

(a + b) (a – b) = a² – b²

(a + b)² = a² + b² + 2ab

______________________________________

(i) (3 + √3) (2 + √2)

3(2+√2) + √3(2+√2)

⇒ 3 × 2 + 3√2+ 2√3+ √3 ×√2

⇒ 6 +3√2 + 2√3 + √6


(ii) (3 + √3) (3 – √3)

[∵ (a + b) (a – b) = a² – b²]

⇒ (3)² – (√3)² (√3×√3=3)
⇒ 9 – 3

⇒ 6


(iii) (√5 + √2)².

[∵ (a + b)² = a² + b² + 2ab]

⇒ (√5)² + (√2)² + 2 ×√5 × √2
⇒ 5 + 2 + 2 × √(5× 2)

⇒ 7 +2√10


(iv) (√5 – √2) (√5 + √2)

[∵ (a + b) (a – b) = a² – b²]

⇒ (√5)² – (√2)²

⇒ 5 – 2

⇒ 3

========================================================================
Hope this will help you....