Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 636 · 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.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
2. 2.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
3. 3.What is 44²? =
4. 4.A square garden has an area of 289 square m. How long is each side (in m)?
5. 5.What is √1681? =
6. 6.How many whole numbers lie between 21² and 22²?
7. 7.Which of these is a perfect square? (a) 1331 (b) 1361 (c) 1296
8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
10. 10.What is 64²? =
11. 11.What is 50²? =
12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √5776? =
14. 14.How many whole numbers lie between 43² and 44²?
15. 15.What is 51²? =
16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
17. 17.How many whole numbers lie between 15² and 16²?
18. 18.What is √2916? =
19. 19.What is the smallest whole number by which 60 must be divided to get a perfect square?
20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
21. 21.How many whole numbers lie between 35² and 36²?
22. 22.What is the smallest whole number by which 80 must be divided to get a perfect square?
23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 676 (b) 688 (c) 726
25. 25.What is √900? =
26. 26.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
27. 27.Which of these is a perfect square? (a) 1225 (b) 1291 (c) 1260
28. 28.A square garden has an area of 100 square m. How long is each side (in m)?
29. 29.What is 65²? =
30. 30.Which of these is a perfect square? (a) 357 (b) 324 (c) 352
31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √5041? =
33. 33.A square garden has an area of 400 square m. How long is each side (in m)?
34. 34.What is √729? =
35. 35.What is 27²? =
36. 36.How many whole numbers lie between 20² and 21²?
37. 37.What is 69²? =
38. 38.Which of these is a perfect square? (a) 105 (b) 100 (c) 110
39. 39.Which of these is a perfect square? (a) 258 (b) 273 (c) 256
40. 40.A square garden has an area of 49 square m. How long is each side (in m)?

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