Question

If \(\sqrt {11\; - 4\surd 7} + \;\sqrt {9 + 2\surd 20} \)  = √a + √b, where a and b are positive integers, then the value of a² - b² =?
1. 40
2. 24
3. 48
4. 42

Answer 1

Correct Answer - Option 2 : 24

Formula used:

(a + b)² = a² + b² + 2ab and

(a - b)² = a² + b² - 2ab

Calculation:

⇒ \(\sqrt {11\; - 2\surd 28} + \;\sqrt {9 + 2\surd 20} \) = √a + √b

⇒ (28 = 7 × 4 and 7 + 4 = 11 as same 20 = 4 × 5 and 4 + 5)

this is followed by above formula so we can write

√7 - √4 + √5 + √4 = √a + √b

⇒ a = 7 and b = 5

Now,

a² - b² = 7² - 5² = 24