Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 231 · 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.How many whole numbers lie between 48² and 49²?
2. 2.What is the smallest whole number by which 208 must be divided to get a perfect square?
3. 3.A square garden has an area of 289 square m. How long is each side (in m)?
4. 4.How many whole numbers lie between 43² and 44²?
5. 5.Which of these is a perfect square? (a) 289 (b) 312 (c) 315
6. 6.What is 86²? =
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 39²? =
9. 9.What is the smallest whole number by which 75 must be divided to get a perfect square?
10. 10.What is √3364? =
11. 11.What is the smallest whole number by which 320 must be divided to get a perfect square?
12. 12.A square garden has an area of 1600 square m. How long is each side (in m)?
13. 13.What is 25²? =
14. 14.How many whole numbers lie between 26² and 27²?
15. 15.Which of these is a perfect square? (a) 532 (b) 529 (c) 575
16. 16.What is √9216? =
17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √5329? =
19. 19.What is 90²? =
20. 20.What is 72²? =
21. 21.What is √3136? =
22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √5625? =
24. 24.Which of these is a perfect square? (a) 1024 (b) 1032 (c) 1076
25. 25.What is 64²? =
26. 26.A square garden has an area of 2809 square m. How long is each side (in m)?
27. 27.Which of these is a perfect square? (a) 701 (b) 683 (c) 676
28. 28.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
29. 29.How many whole numbers lie between 38² and 39²?
30. 30.A square garden has an area of 1764 square m. How long is each side (in m)?
31. 31.How many whole numbers lie between 31² and 32²?
32. 32.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
33. 33.What is √361? =
34. 34.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 81 square m. How long is each side (in m)?
37. 37.What is √4225? =
38. 38.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
39. 39.What is 15²? =
40. 40.A square garden has an area of 2401 square m. How long is each side (in m)?

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