Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 456 · 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) 1523 (b) 1521 (c) 1526
2. 2.How many whole numbers lie between 6² and 7²?
3. 3.What is 87²? =
4. 4.How many whole numbers lie between 17² and 18²?
5. 5.What is √1849? =
6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 1677 (b) 1643 (c) 1600
8. 8.Which of these is a perfect square? (a) 1446 (b) 1444 (c) 1496
9. 9.Which of these is a perfect square? (a) 291 (b) 320 (c) 289
10. 10.What is 90²? =
11. 11.What is √1296? =
12. 12.What is √361? =
13. 13.What is the smallest whole number by which 128 must be divided to get a perfect square?
14. 14.Which of these is a perfect square? (a) 176 (b) 169 (c) 184
15. 15.How many whole numbers lie between 44² and 45²?
16. 16.What is √324? =
17. 17.What is 85²? =
18. 18.Which of these is a perfect square? (a) 167 (b) 144 (c) 164
19. 19.What is √4624? =
20. 20.What is the smallest whole number by which 468 must be divided to get a perfect square?
21. 21.Which of these is a perfect square? (a) 432 (b) 400 (c) 420
22. 22.What is 50²? =
23. 23.What is 27²? =
24. 24.A square garden has an area of 324 square m. How long is each side (in m)?
25. 25.A square garden has an area of 64 square m. How long is each side (in m)?
26. 26.How many whole numbers lie between 23² and 24²?
27. 27.A square garden has an area of 3025 square m. How long is each side (in m)?
28. 28.Which of these is a perfect square? (a) 507 (b) 505 (c) 484
29. 29.What is √4225? =
30. 30.What is 30²? =
31. 31.What is √841? =
32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
34. 34.What is 64²? =
35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
36. 36.Which of these is a perfect square? (a) 479 (b) 441 (c) 461
37. 37.What is the smallest whole number by which 45 must be divided to get a perfect square?
38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 76²? =
40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?

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