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4. Find the square roots of the following numbers by the Prime Factorisation Method. i. 729 ii. 400 iii. 1764

4. Find the square roots of the following numbers by the Prime Factorisation Method. i. 729 ii. 400 iii. 1764  

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

Thanks

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