Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 407 · 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 16²? =
2. 2.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
3. 3.What is the smallest whole number by which 1053 must be divided to get a perfect square?
4. 4.A square garden has an area of 841 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 40² and 41²?
6. 6.What is √5929? =
7. 7.A square garden has an area of 361 square m. How long is each side (in m)?
8. 8.Which of these is a perfect square? (a) 478 (b) 443 (c) 441
9. 9.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
10. 10.What is √1225? =
11. 11.How many whole numbers lie between 29² and 30²?
12. 12.What is 56²? =
13. 13.How many whole numbers lie between 9² and 10²?
14. 14.Which of these is a perfect square? (a) 238 (b) 225 (c) 246
15. 15.What is 29²? =
16. 16.What is √3969? =
17. 17.What is 51²? =
18. 18.Which of these is a perfect square? (a) 537 (b) 529 (c) 549
19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
20. 20.What is 37²? =
21. 21.What is √1089? =
22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
24. 24.What is 25²? =
25. 25.Which of these is a perfect square? (a) 354 (b) 324 (c) 339
26. 26.A square garden has an area of 900 square m. How long is each side (in m)?
27. 27.What is 48²? =
28. 28.What is the smallest whole number by which 125 must be divided to get a perfect square?
29. 29.A square garden has an area of 81 square m. How long is each side (in m)?
30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
31. 31.A square garden has an area of 3249 square m. How long is each side (in m)?
32. 32.How many whole numbers lie between 28² and 29²?
33. 33.What is the smallest whole number by which 48 must be divided to get a perfect square?
34. 34.A square garden has an area of 729 square m. How long is each side (in m)?
35. 35.What is √9604? =
36. 36.How many whole numbers lie between 32² and 33²?
37. 37.What is √5776? =
38. 38.What is √225? =
39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
40. 40.What is 95²? =

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