9 + \(2\sqrt{14}\) का वर्गमूल कितना है?

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Territorial Army Official Paper I (Conducted on 25 Sep 2022)
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  1. 1 + \(2\sqrt 2\)
  2. \(\sqrt 3\)\(\sqrt 6\)
  3. \(\sqrt 2\)\(\sqrt 7\)
  4. \(\sqrt 2\)\(\sqrt 5\)

Answer (Detailed Solution Below)

Option 3 : \(\sqrt 2\)\(\sqrt 7\)
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Detailed Solution

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दिया गया है:

9 + \(2√{14}\) का वर्गमूल है

प्रयुक्त अवधारणा: 

(a + b)2 = a2 + b2 + 2ab 

गणना:

हमारे पास है, 

 9 + \(2√{14}\) 

⇒ 2 + 7 + 2√(2 × 7)

⇒ (√2)2 + (√7)2 + 2 × √2 × √7

अब, उपरोक्त अवधारणा के अनुसार,

⇒ (√2 + √7)2

∴ अभीष्ट वर्गमूल √2 + √7 है। 

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