Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 97 · 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 √7225? =
2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √8836? =
4. 4.What is 72²? =
5. 5.Which of these is a perfect square? (a) 452 (b) 441 (c) 458
6. 6.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
7. 7.A square garden has an area of 2401 square m. How long is each side (in m)?
8. 8.What is √3969? =
9. 9.A square garden has an area of 169 square m. How long is each side (in m)?
10. 10.A square garden has an area of 64 square m. How long is each side (in m)?
11. 11.What is √625? =
12. 12.Which of these is a perfect square? (a) 1600 (b) 1635 (c) 1660
13. 13.How many whole numbers lie between 48² and 49²?
14. 14.How many whole numbers lie between 45² and 46²?
15. 15.How many whole numbers lie between 16² and 17²?
16. 16.What is 36²? =
17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 1119 (b) 1116 (c) 1089
20. 20.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
21. 21.What is 26²? =
22. 22.What is 13²? =
23. 23.What is 16²? =
24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
25. 25.What is 98²? =
26. 26.Which of these is a perfect square? (a) 301 (b) 289 (c) 309
27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
29. 29.What is √7396? =
30. 30.A square garden has an area of 2704 square m. How long is each side (in m)?
31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
32. 32.How many whole numbers lie between 29² and 30²?
33. 33.What is 30²? =
34. 34.Which of these is a perfect square? (a) 1296 (b) 1368 (c) 1315
35. 35.What is 34²? =
36. 36.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
37. 37.How many whole numbers lie between 41² and 42²?
38. 38.What is 60²? =
39. 39.What is 64²? =
40. 40.A square garden has an area of 100 square m. How long is each side (in m)?

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