Question

Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\). Then √x is equal to:
1. 4/9
2. 5/9
3. 5/12
4. 7/12

Answer 1

Correct Answer - Option 3 : 5/12

Given :- 

\(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} ÷ \frac{{√ {1200} }}{{√ 768}}} \right) × \frac{{√ {175} }}{{√ {1792} }}\)

Calculation :-

⇒ √1875 = √(625 × 3) = 25√3

⇒ √3888 = √(1296 × 3) = 36√3

⇒ √1200 = √(400 × 3) = 20√3

⇒ √768 = √(256 × 3) = 16√3 

⇒ √175 = √(25 × 7) = 5√7

⇒ √1792 = √(256 × 7) = 16√7

⇒ x = [(25√3/36√3) ÷ (20√3/16√3)] × (5√7/16√7)

⇒ x = (25/36) × (16/20) × (5/16)

⇒ x = (25/(36 × 4))

⇒ √x = √(25/(36 × 4))

⇒ √x = (5/12)

∴ √x is (5/12)