Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 463 · 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 the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 32²? =
3. 3.Which of these is a perfect square? (a) 325 (b) 330 (c) 324
4. 4.What is 79²? =
5. 5.What is 23²? =
6. 6.A square garden has an area of 1936 square m. How long is each side (in m)?
7. 7.How many whole numbers lie between 39² and 40²?
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 810 must be divided to get a perfect square?
10. 10.A square garden has an area of 3364 square m. How long is each side (in m)?
11. 11.Which of these is a perfect square? (a) 625 (b) 668 (c) 650
12. 12.Which of these is a perfect square? (a) 1369 (b) 1376 (c) 1438
13. 13.What is √4761? =
14. 14.Which of these is a perfect square? (a) 1131 (b) 1136 (c) 1089
15. 15.What is √324? =
16. 16.How many whole numbers lie between 10² and 11²?
17. 17.What is 17²? =
18. 18.What is 70²? =
19. 19.What is √361? =
20. 20.What is √1296? =
21. 21.Which of these is a perfect square? (a) 800 (b) 805 (c) 784
22. 22.What is √196? =
23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
24. 24.What is √7744? =
25. 25.Which of these is a perfect square? (a) 529 (b) 571 (c) 530
26. 26.What is the smallest whole number by which 896 must be divided to get a perfect square?
27. 27.A square garden has an area of 2704 square m. How long is each side (in m)?
28. 28.A square garden has an area of 2401 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 17² and 18²?
30. 30.A square garden has an area of 289 square m. How long is each side (in m)?
31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
32. 32.A square garden has an area of 81 square m. How long is each side (in m)?
33. 33.What is √1444? =
34. 34.How many whole numbers lie between 23² and 24²?
35. 35.How many whole numbers lie between 48² and 49²?
36. 36.Which of these is a perfect square? (a) 172 (b) 169 (c) 171
37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
40. 40.What is √1024? =

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