Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 641 · 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 25² and 26²?
2. 2.What is 95²? =
3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
4. 4.How many whole numbers lie between 15² and 16²?
5. 5.What is 36²? =
6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 47²? =
8. 8.What is √169? =
9. 9.How many whole numbers lie between 34² and 35²?
10. 10.Which of these is a perfect square? (a) 108 (b) 100 (c) 102
11. 11.What is 37²? =
12. 12.What is 73²? =
13. 13.A square garden has an area of 3600 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 7² and 8²?
15. 15.What is √225? =
16. 16.How many whole numbers lie between 27² and 28²?
17. 17.A square garden has an area of 2916 square m. How long is each side (in m)?
18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
19. 19.How many whole numbers lie between 45² and 46²?
20. 20.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
21. 21.How many whole numbers lie between 8² and 9²?
22. 22.A square garden has an area of 784 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 492 (b) 520 (c) 484
24. 24.Which of these is a perfect square? (a) 399 (b) 361 (c) 381
25. 25.How many whole numbers lie between 42² and 43²?
26. 26.What is 67²? =
27. 27.What is √1225? =
28. 28.What is √5929? =
29. 29.How many whole numbers lie between 18² and 19²?
30. 30.A square garden has an area of 169 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 310 (b) 289 (c) 293
32. 32.A square garden has an area of 144 square m. How long is each side (in m)?
33. 33.How many whole numbers lie between 40² and 41²?
34. 34.What is √2704? =
35. 35.Which of these is a perfect square? (a) 1600 (b) 1663 (c) 1618
36. 36.What is 48²? =
37. 37.What is √484? =
38. 38.What is the smallest whole number by which 1215 must be divided to get a perfect square?
39. 39.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
40. 40.How many whole numbers lie between 16² and 17²?

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