Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 253 · 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.A square garden has an area of 2025 square m. How long is each side (in m)?
2. 2.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
3. 3.A square garden has an area of 121 square m. How long is each side (in m)?
4. 4.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
5. 5.A square garden has an area of 3600 square m. How long is each side (in m)?
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 1296 square m. How long is each side (in m)?
8. 8.What is 98²? =
9. 9.Which of these is a perfect square? (a) 370 (b) 399 (c) 361
10. 10.What is 88²? =
11. 11.What is √2500? =
12. 12.What is 48²? =
13. 13.How many whole numbers lie between 9² and 10²?
14. 14.A square garden has an area of 3364 square m. How long is each side (in m)?
15. 15.Which of these is a perfect square? (a) 225 (b) 235 (c) 229
16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
17. 17.A square garden has an area of 144 square m. How long is each side (in m)?
18. 18.What is √7744? =
19. 19.How many whole numbers lie between 15² and 16²?
20. 20.Which of these is a perfect square? (a) 1633 (b) 1657 (c) 1600
21. 21.How many whole numbers lie between 8² and 9²?
22. 22.What is √9409? =
23. 23.What is 65²? =
24. 24.A square garden has an area of 484 square m. How long is each side (in m)?
25. 25.What is 75²? =
26. 26.Which of these is a perfect square? (a) 1359 (b) 1351 (c) 1296
27. 27.What is the smallest whole number by which 735 must be divided to get a perfect square?
28. 28.What is √8836? =
29. 29.A square garden has an area of 225 square m. How long is each side (in m)?
30. 30.What is 20²? =
31. 31.What is √1936? =
32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √5776? =
34. 34.What is 95²? =
35. 35.What is 13²? =
36. 36.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
37. 37.What is 76²? =
38. 38.What is √2025? =
39. 39.What is √576? =
40. 40.Which of these is a perfect square? (a) 1156 (b) 1219 (c) 1173

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