Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 31 · 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 √529? =
2. 2.Which of these is a perfect square? (a) 1225 (b) 1276 (c) 1251
3. 3.What is the smallest whole number by which 396 must be divided to get a perfect square?
4. 4.Which of these is a perfect square? (a) 253 (b) 243 (c) 225
5. 5.What is √225? =
6. 6.A square garden has an area of 361 square m. How long is each side (in m)?
7. 7.What is √121? =
8. 8.What is the smallest whole number by which 250 must be divided to get a perfect square?
9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
10. 10.How many whole numbers lie between 11² and 12²?
11. 11.What is 98²? =
12. 12.How many whole numbers lie between 43² and 44²?
13. 13.What is 36²? =
14. 14.How many whole numbers lie between 27² and 28²?
15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
16. 16.A square garden has an area of 1225 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 23² and 24²?
18. 18.A square garden has an area of 2116 square m. How long is each side (in m)?
19. 19.What is √5929? =
20. 20.What is the smallest whole number by which 896 must be divided to get a perfect square?
21. 21.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
22. 22.What is 62²? =
23. 23.Which of these is a perfect square? (a) 149 (b) 150 (c) 144
24. 24.What is the smallest whole number by which 1053 must be divided to get a perfect square?
25. 25.What is 91²? =
26. 26.Which of these is a perfect square? (a) 529 (b) 571 (c) 543
27. 27.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
28. 28.What is 43²? =
29. 29.A square garden has an area of 225 square m. How long is each side (in m)?
30. 30.What is √5625? =
31. 31.What is √5041? =
32. 32.What is 65²? =
33. 33.How many whole numbers lie between 45² and 46²?
34. 34.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √4225? =
36. 36.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
37. 37.How many whole numbers lie between 38² and 39²?
38. 38.How many whole numbers lie between 29² and 30²?
39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
40. 40.What is 66²? =

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