Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 574 · 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.Which of these is a perfect square? (a) 331 (b) 324 (c) 359
2. 2.What is √6724? =
3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 94²? =
5. 5.Which of these is a perfect square? (a) 230 (b) 225 (c) 247
6. 6.What is √3600? =
7. 7.What is √2116? =
8. 8.What is the smallest whole number by which 32 must be divided to get a perfect square?
9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
10. 10.How many whole numbers lie between 10² and 11²?
11. 11.How many whole numbers lie between 15² and 16²?
12. 12.Which of these is a perfect square? (a) 1070 (b) 1024 (c) 1033
13. 13.What is √961? =
14. 14.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
15. 15.What is 51²? =
16. 16.What is √4489? =
17. 17.What is 61²? =
18. 18.What is √400? =
19. 19.How many whole numbers lie between 35² and 36²?
20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 80²? =
22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
23. 23.A square garden has an area of 100 square m. How long is each side (in m)?
24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
25. 25.A square garden has an area of 1156 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 75 must be divided to get a perfect square?
27. 27.A square garden has an area of 144 square m. How long is each side (in m)?
28. 28.What is 29²? =
29. 29.What is 83²? =
30. 30.What is 22²? =
31. 31.What is √7569? =
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
33. 33.Which of these is a perfect square? (a) 1289 (b) 1240 (c) 1225
34. 34.What is √6084? =
35. 35.What is 13²? =
36. 36.How many whole numbers lie between 9² and 10²?
37. 37.What is 17²? =
38. 38.A square garden has an area of 3481 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 1156 (b) 1171 (c) 1162
40. 40.What is √8100? =

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