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CBSE Maths · Class 8

Chapter 6: Squares and Square Roots

Name: ________________________
Date: ______________
Marks: ____ / 10

Perfect squares; finding square roots by prime factorisation and long division.

Questions

  1. 225\sqrt{225}.
  2. Smallest number to divide 29252925 so quotient is a perfect square.
  3. 1225\sqrt{1225}.
  4. 144\sqrt{144}.
  5. 2025\sqrt{2025}.
  6. Is 1717 a perfect square?
  7. 6.25\sqrt{6.25}.
  8. Smallest number to multiply 180180 to make a perfect square.
  9. Square of 9999.
  10. 225\sqrt{225}.

Extra Practice (Optional)

  • Sum of first 1010 odd numbers is a perfect square. Verify.
  • 2916\sqrt{2916}.
  • Is 1000010000 a perfect square?

Answer Key (For Teachers)

  1. Answer: 1515.
    Working: 152=22515^2=225.
  2. Answer: 1313.
    Working: 2925=3252132925 = 3^2\cdot 5^2\cdot 13; divide by 1313.
  3. Answer: 3535.
    Working: 352=122535^2 = 1225.
  4. Answer: 1212
    Working: 12212^2.
  5. Answer: 4545
    Working: 45245^2.
  6. Answer: No.
    Working: No — square roots not integer.
  7. Answer: 2.52.5
    Working: 2.522.5^2.
  8. Answer: 55
    Working: 180=22325180 = 2^2\cdot 3^2\cdot 5; need factor of 55.
  9. Answer: 98019801
    Working: (1001)2(100-1)^2.
  10. Answer: 1515
    Working: 15215^2.
Gyaan Maths · CBSE Class 8 · Chapter 6
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026