Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 554 · 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 14² and 15²?
2. 2.What is √6241? =
3. 3.What is 87²? =
4. 4.A square garden has an area of 961 square m. How long is each side (in m)?
5. 5.What is √3025? =
6. 6.What is the smallest whole number by which 63 must be divided to get a perfect square?
7. 7.A square garden has an area of 144 square m. How long is each side (in m)?
8. 8.What is √225? =
9. 9.Which of these is a perfect square? (a) 487 (b) 518 (c) 484
10. 10.Which of these is a perfect square? (a) 546 (b) 561 (c) 529
11. 11.A square garden has an area of 576 square m. How long is each side (in m)?
12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
14. 14.What is 98²? =
15. 15.What is √2401? =
16. 16.What is 76²? =
17. 17.Which of these is a perfect square? (a) 121 (b) 122 (c) 139
18. 18.How many whole numbers lie between 44² and 45²?
19. 19.What is √4356? =
20. 20.How many whole numbers lie between 5² and 6²?
21. 21.How many whole numbers lie between 43² and 44²?
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √625? =
24. 24.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
25. 25.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
26. 26.What is √5041? =
27. 27.A square garden has an area of 1369 square m. How long is each side (in m)?
28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 357 (b) 337 (c) 324
30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
31. 31.How many whole numbers lie between 18² and 19²?
32. 32.A square garden has an area of 49 square m. How long is each side (in m)?
33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 30² and 31²?
35. 35.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 1600 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
38. 38.What is √8649? =
39. 39.What is 30²? =
40. 40.What is the smallest whole number by which 125 must be divided to get a perfect square?

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