Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 675 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.Which of these is a perfect square? (a) 900 (b) 941 (c) 937
2. 2.What is 82²? =
3. 3.What is 46²? =
4. 4.What is √1600? =
5. 5.How many whole numbers lie between 7² and 8²?
6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 27²? =
8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
9. 9.Which of these is a perfect square? (a) 885 (b) 841 (c) 880
10. 10.Which of these is a perfect square? (a) 576 (b) 620 (c) 606
11. 11.What is 80²? =
12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 37² and 38²?
14. 14.How many whole numbers lie between 40² and 41²?
15. 15.What is √4900? =
16. 16.What is the smallest whole number by which 40 must be divided to get a perfect square?
17. 17.Which of these is a perfect square? (a) 174 (b) 183 (c) 169
18. 18.What is 84²? =
19. 19.What is 77²? =
20. 20.What is √4489? =
21. 21.What is the smallest whole number by which 360 must be divided to get a perfect square?
22. 22.What is 12²? =
23. 23.What is 90²? =
24. 24.What is the smallest whole number by which 567 must be divided to get a perfect square?
25. 25.What is 39²? =
26. 26.What is √1089? =
27. 27.What is 58²? =
28. 28.Which of these is a perfect square? (a) 1603 (b) 1600 (c) 1633
29. 29.What is √2025? =
30. 30.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
31. 31.Which of these is a perfect square? (a) 784 (b) 840 (c) 800
32. 32.What is 15²? =
33. 33.A square garden has an area of 1521 square m. How long is each side (in m)?
34. 34.What is 20²? =
35. 35.What is 38²? =
36. 36.A square garden has an area of 1296 square m. How long is each side (in m)?
37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
38. 38.What is 92²? =
39. 39.How many whole numbers lie between 46² and 47²?
40. 40.Which of these is a perfect square? (a) 243 (b) 225 (c) 249

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