1.

Find the square root of 23 + 8√7.1. 2√2 + 72. 2√2 + √73. 4 + √74. 4 – √7

Answer» Correct Answer - Option 3 : 4 + √7

Given:

The number is 23 + 8√7

Identity used:

(a + b)2 = a2 + b2 + 2ab

Calculation:

The number can be written as 23 + 2 × 4√7 

⇒ 23 + 8√7 = 23 + 2√(16 × 7)

⇒ 23 + 8√7 = 16 + 7 + 2√(16 × 7)

⇒ 23 + 8√7 = 42 + √7 + 2 × 4 × √7

⇒ 23 + 8√7 = (4 + √7)2 

√(23 + 8√7) = √(4 + √7)2 

⇒ √(23 + 8√7) = 4 + √7

∴ Square root of 23 + 8√7 is 4 + √7



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