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4. Find the square roots of the following numbers by the Prime Factorisation Method iv. 4096 v. 7744 vi. 9604

4. Find the square roots of the following numbers by the Prime Factorisation Method  iv. 4096 v. 7744 vi. 9604 

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student


729 = 3×3×3×3×3×3×1
⇒ 729 = (3×3)×(3×3)×(3×3) ⇒ 729 = (3×3×3)×(3×3×3) ⇒ 729 = (3×3×3)2⇒√729=3×3×3=27

400 = 2×2×2×2×5×5×1
⇒ 400 = (2×2)×(2×2)×(5×5) ⇒400 = (2×2×5)×(2×2×5)⇒ 400 = (2×2×5)2⇒√400=2×2×5=20

1764 = 2×2×3×3×7×7
⇒ 1764 = (2×2)×(3×3)×(7×7) ⇒ 1764 = (2×3×7)×(2×3×7) ⇒ 1764 = (2×3×7)2⇒√1764=2×3×7=42

4096 = 2×2×2×2×2×2×2×2×2×2×2×2
⇒ 4096 = (2×2)×(2×2)×(2×2)×(2×2)×(2×2)×(2×2) ⇒ 4096 = (2×2×2×2×2×2)×(2×2×2×2×2×2)
⇒ 4096 = (2×2×2×2×2×2)2
⇒ √4096 = 2×2×2 ×2×2×2 = 64

7744 = 2×2×2×2×2×2×11×11×1
⇒ 7744 = (2×2)×(2×2)×(2×2)×(11×11)
⇒ 7744 = (2×2×2×11)×(2×2×2×11)
⇒ 7744 = (2×2×2×11)2
⇒ √7744 = 2×2×2×11 = 88


9604=62×2×7×7×7×7
9604=(2×7×7)×(2×7×7)
⇒9604=(2×7×7)2
⇒√9604=2×7×7=98

Thanks

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