The square root of 33 – 4√35 is :

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The square root of 33 – 4√35 is :

1. ±(2√7 + √5)
2. ±(√7 + 2√5)
3. ±(√7 − 2√5)
4. ±(2√7 − √5)

Correct Option: D

33 – 4√35
= 33 – 2 × 2√5 × 7
= 33 – 2 × 2√7 × √5
= 28 + 5 – 2 × 2 √7 × √5
= (2√7)² + (√5)² – 2 × 2 √7 × √5
= (2√7 − √5)²
∴ √33 − 4√35
= √(2√7 − √5)²
= ±(2√7 − √5)