If \(\sqrt{768}\) × \(\sqrt{3267}\) = 44 × y, then the value of

1.	If \(\sqrt{768}\) × \(\sqrt{3267}\) = 44 × y, then the value of y:1. 442. 723. 884. 36
Answer» Correct Answer - Option 4 : 36 Given: \(√{768}\) × \(√{3267}\) = 44 × y Firmulae required: (a^m)ⁿ= a^mn √a = a^1/2 a^m× b^m= (a × b)^m Calculations: Factors of 768 = 256 × 3 ⇒ 2⁸× 3 (∵ 256 = 2⁸) Factors of 3267 = 121 × 27 ⇒ 11² × 3³ (∵ 121 = 11² , 3³ = 27) ⇒ (768)^1/2 × (3267)^1/2 = 44 × y ⇒ (28 × 3 × 112 × 33)^1/2 = 44 × y ⇒ (2⁸× 3⁴ × 11² )^1/2 = 44 × y ⇒ 2^{8 × 1/2}× 3⁴^{× 1/2} × 11^2 ×1/2 = 44 × y ⇒ 2⁴ × 3² × 11 = 44 × y ⇒ 16 × 9 × 11 = 44 × y ⇒ y = 9 × 4 = 36 ∴ The value of y is 36

If \(\sqrt{768}\) × \(\sqrt{3267}\) = 44 × y, then the value of y:1. 442. 723. 884. 36

Answer» Correct Answer - Option 4 : 36

Given:

\(√{768}\) × \(√{3267}\) = 44 × y

Firmulae required:

(a^m)ⁿ= a^mn

√a = a^1/2

a^m× b^m= (a × b)^m

Calculations:

Factors of 768 = 256 × 3

⇒ 2⁸× 3 (∵ 256 = 2⁸)

Factors of 3267 = 121 × 27

⇒ 11² × 3³ (∵ 121 = 11² , 3³ = 27)

⇒ (768)^1/2 × (3267)^1/2 = 44 × y

⇒ (28 × 3 × 112 × 33)^1/2 = 44 × y

⇒ (2⁸× 3⁴ × 11² )^1/2 = 44 × y

⇒ 2^{8 × 1/2}× 3⁴^{× 1/2} × 11^2 ×1/2 = 44 × y

⇒ 2⁴ × 3² × 11 = 44 × y

⇒ 16 × 9 × 11 = 44 × y

⇒ y = 9 × 4 = 36

∴ The value of y is 36