Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 708 · 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 √900? =
2. 2.What is 92²? =
3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 22²? =
5. 5.A square garden has an area of 2025 square m. How long is each side (in m)?
6. 6.What is the smallest whole number by which 252 must be divided to get a perfect square?
7. 7.How many whole numbers lie between 45² and 46²?
8. 8.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
9. 9.What is 71²? =
10. 10.What is √1681? =
11. 11.A square garden has an area of 225 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 80 must be divided to get a perfect square?
13. 13.What is 28²? =
14. 14.A square garden has an area of 841 square m. How long is each side (in m)?
15. 15.Which of these is a perfect square? (a) 1369 (b) 1427 (c) 1399
16. 16.What is √121? =
17. 17.Which of these is a perfect square? (a) 519 (b) 494 (c) 484
18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
19. 19.A square garden has an area of 121 square m. How long is each side (in m)?
20. 20.How many whole numbers lie between 21² and 22²?
21. 21.Which of these is a perfect square? (a) 1225 (b) 1292 (c) 1268
22. 22.What is 84²? =
23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √8649? =
25. 25.How many whole numbers lie between 12² and 13²?
26. 26.What is √576? =
27. 27.What is √2116? =
28. 28.What is √784? =
29. 29.A square garden has an area of 900 square m. How long is each side (in m)?
30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 37²? =
32. 32.Which of these is a perfect square? (a) 317 (b) 289 (c) 304
33. 33.What is √5929? =
34. 34.A square garden has an area of 3136 square m. How long is each side (in m)?
35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
37. 37.How many whole numbers lie between 15² and 16²?
38. 38.What is 47²? =
39. 39.What is 99²? =
40. 40.What is 35²? =

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