Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 192 · 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.How many whole numbers lie between 39² and 40²?
2. 2.What is √4225? =
3. 3.What is √9216? =
4. 4.A square garden has an area of 2809 square m. How long is each side (in m)?
5. 5.Which of these is a perfect square? (a) 292 (b) 289 (c) 323
6. 6.Which of these is a perfect square? (a) 1104 (b) 1100 (c) 1089
7. 7.What is 28²? =
8. 8.How many whole numbers lie between 14² and 15²?
9. 9.Which of these is a perfect square? (a) 594 (b) 587 (c) 576
10. 10.What is 33²? =
11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
12. 12.A square garden has an area of 100 square m. How long is each side (in m)?
13. 13.What is √196? =
14. 14.What is the smallest whole number by which 160 must be divided to get a perfect square?
15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 42² and 43²?
17. 17.What is 31²? =
18. 18.Which of these is a perfect square? (a) 159 (b) 160 (c) 144
19. 19.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
21. 21.How many whole numbers lie between 33² and 34²?
22. 22.A square garden has an area of 1225 square m. How long is each side (in m)?
23. 23.What is 62²? =
24. 24.A square garden has an area of 1024 square m. How long is each side (in m)?
25. 25.What is 68²? =
26. 26.What is √8464? =
27. 27.What is √8649? =
28. 28.What is √8100? =
29. 29.What is 67²? =
30. 30.Which of these is a perfect square? (a) 1653 (b) 1652 (c) 1600
31. 31.What is the smallest whole number by which 32 must be divided to get a perfect square?
32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
33. 33.What is 75²? =
34. 34.What is the smallest whole number by which 896 must be divided to get a perfect square?
35. 35.What is 70²? =
36. 36.How many whole numbers lie between 37² and 38²?
37. 37.Which of these is a perfect square? (a) 130 (b) 135 (c) 121
38. 38.What is 63²? =
39. 39.How many whole numbers lie between 32² and 33²?
40. 40.Which of these is a perfect square? (a) 377 (b) 383 (c) 361

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