Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 730 · 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 79²? =
2. 2.What is 17²? =
3. 3.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
4. 4.A square garden has an area of 529 square m. How long is each side (in m)?
5. 5.What is the smallest whole number by which 12 must be divided to get a perfect square?
6. 6.A square garden has an area of 2116 square m. How long is each side (in m)?
7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 62²? =
9. 9.A square garden has an area of 169 square m. How long is each side (in m)?
10. 10.What is √3721? =
11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 247 (b) 225 (c) 229
13. 13.A square garden has an area of 1444 square m. How long is each side (in m)?
14. 14.What is the smallest whole number by which 250 must be divided to get a perfect square?
15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √4624? =
17. 17.How many whole numbers lie between 15² and 16²?
18. 18.What is the smallest whole number by which 24 must be divided to get a perfect square?
19. 19.What is 33²? =
20. 20.How many whole numbers lie between 40² and 41²?
21. 21.Which of these is a perfect square? (a) 742 (b) 729 (c) 782
22. 22.What is 76²? =
23. 23.A square garden has an area of 2916 square m. How long is each side (in m)?
24. 24.What is the smallest whole number by which 891 must be divided to get a perfect square?
25. 25.What is 86²? =
26. 26.What is √5776? =
27. 27.A square garden has an area of 3249 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 31² and 32²?
29. 29.Which of these is a perfect square? (a) 418 (b) 400 (c) 408
30. 30.What is 31²? =
31. 31.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 289 (b) 291 (c) 292
33. 33.A square garden has an area of 36 square m. How long is each side (in m)?
34. 34.What is √2500? =
35. 35.What is 88²? =
36. 36.What is 97²? =
37. 37.What is 77²? =
38. 38.Which of these is a perfect square? (a) 1612 (b) 1601 (c) 1600
39. 39.What is 39²? =
40. 40.How many whole numbers lie between 13² and 14²?

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