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