Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 393 · 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 √3136? =
2. 2.What is √4489? =
3. 3.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
4. 4.Which of these is a perfect square? (a) 820 (b) 824 (c) 784
5. 5.What is 24²? =
6. 6.A square garden has an area of 441 square m. How long is each side (in m)?
7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
8. 8.How many whole numbers lie between 11² and 12²?
9. 9.What is 65²? =
10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 2025 square m. How long is each side (in m)?
12. 12.How many whole numbers lie between 10² and 11²?
13. 13.A square garden has an area of 3249 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 12² and 13²?
15. 15.What is the smallest whole number by which 45 must be divided to get a perfect square?
16. 16.What is 83²? =
17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
18. 18.A square garden has an area of 1225 square m. How long is each side (in m)?
19. 19.A square garden has an area of 1369 square m. How long is each side (in m)?
20. 20.A square garden has an area of 49 square m. How long is each side (in m)?
21. 21.What is 42²? =
22. 22.What is √324? =
23. 23.What is √361? =
24. 24.What is 38²? =
25. 25.What is √784? =
26. 26.Which of these is a perfect square? (a) 255 (b) 225 (c) 237
27. 27.What is √2116? =
28. 28.A square garden has an area of 289 square m. How long is each side (in m)?
29. 29.A square garden has an area of 121 square m. How long is each side (in m)?
30. 30.What is 99²? =
31. 31.Which of these is a perfect square? (a) 1296 (b) 1309 (c) 1333
32. 32.A square garden has an area of 256 square m. How long is each side (in m)?
33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 1936 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 1176 (b) 1156 (c) 1220
36. 36.What is 34²? =
37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 504 must be divided to get a perfect square?
39. 39.How many whole numbers lie between 48² and 49²?
40. 40.What is 59²? =

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