Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 108 · 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 20² and 21²?
2. 2.How many whole numbers lie between 18² and 19²?
3. 3.A square garden has an area of 1681 square m. How long is each side (in m)?
4. 4.What is 78²? =
5. 5.How many whole numbers lie between 17² and 18²?
6. 6.A square garden has an area of 1369 square m. How long is each side (in m)?
7. 7.What is 23²? =
8. 8.How many whole numbers lie between 44² and 45²?
9. 9.What is 68²? =
10. 10.How many whole numbers lie between 8² and 9²?
11. 11.What is 76²? =
12. 12.How many whole numbers lie between 25² and 26²?
13. 13.What is 48²? =
14. 14.What is 96²? =
15. 15.How many whole numbers lie between 11² and 12²?
16. 16.Which of these is a perfect square? (a) 144 (b) 148 (c) 164
17. 17.What is the smallest whole number by which 192 must be divided to get a perfect square?
18. 18.Which of these is a perfect square? (a) 228 (b) 245 (c) 225
19. 19.What is √5929? =
20. 20.How many whole numbers lie between 34² and 35²?
21. 21.What is 88²? =
22. 22.What is √4900? =
23. 23.What is 33²? =
24. 24.Which of these is a perfect square? (a) 289 (b) 293 (c) 319
25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
26. 26.Which of these is a perfect square? (a) 1156 (b) 1162 (c) 1180
27. 27.What is 83²? =
28. 28.What is √4096? =
29. 29.How many whole numbers lie between 7² and 8²?
30. 30.What is √729? =
31. 31.What is 90²? =
32. 32.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
33. 33.Which of these is a perfect square? (a) 263 (b) 256 (c) 286
34. 34.How many whole numbers lie between 9² and 10²?
35. 35.A square garden has an area of 3481 square m. How long is each side (in m)?
36. 36.What is √9604? =
37. 37.Which of these is a perfect square? (a) 1467 (b) 1460 (c) 1444
38. 38.How many whole numbers lie between 27² and 28²?
39. 39.A square garden has an area of 3249 square m. How long is each side (in m)?
40. 40.What is 86²? =

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