Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 648 · 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) 126 (b) 123 (c) 121
2. 2.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 30²? =
4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
5. 5.What is √6561? =
6. 6.What is √4356? =
7. 7.Which of these is a perfect square? (a) 931 (b) 960 (c) 900
8. 8.What is √4624? =
9. 9.How many whole numbers lie between 36² and 37²?
10. 10.Which of these is a perfect square? (a) 1101 (b) 1123 (c) 1089
11. 11.What is the smallest whole number by which 1215 must be divided to get a perfect square?
12. 12.A square garden has an area of 49 square m. How long is each side (in m)?
13. 13.What is 76²? =
14. 14.How many whole numbers lie between 35² and 36²?
15. 15.How many whole numbers lie between 25² and 26²?
16. 16.What is 25²? =
17. 17.How many whole numbers lie between 45² and 46²?
18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 1081 (b) 1024 (c) 1036
20. 20.What is 86²? =
21. 21.What is √9409? =
22. 22.A square garden has an area of 256 square m. How long is each side (in m)?
23. 23.What is √4225? =
24. 24.Which of these is a perfect square? (a) 1383 (b) 1391 (c) 1369
25. 25.What is 43²? =
26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √8100? =
28. 28.Which of these is a perfect square? (a) 784 (b) 810 (c) 834
29. 29.What is √1225? =
30. 30.What is √6084? =
31. 31.A square garden has an area of 576 square m. How long is each side (in m)?
32. 32.What is 51²? =
33. 33.Which of these is a perfect square? (a) 344 (b) 339 (c) 324
34. 34.A square garden has an area of 3600 square m. How long is each side (in m)?
35. 35.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
36. 36.How many whole numbers lie between 5² and 6²?
37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
39. 39.How many whole numbers lie between 48² and 49²?
40. 40.What is √9801? =

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