Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 292 · 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.Which of these is a perfect square? (a) 498 (b) 484 (c) 528
2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √2401? =
4. 4.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
5. 5.What is the smallest whole number by which 147 must be divided to get a perfect square?
6. 6.A square garden has an area of 2809 square m. How long is each side (in m)?
7. 7.What is the smallest whole number by which 1053 must be divided to get a perfect square?
8. 8.Which of these is a perfect square? (a) 157 (b) 148 (c) 144
9. 9.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
10. 10.Which of these is a perfect square? (a) 745 (b) 780 (c) 729
11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
13. 13.What is 53²? =
14. 14.What is √1225? =
15. 15.What is √2916? =
16. 16.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
17. 17.What is √8100? =
18. 18.What is 77²? =
19. 19.What is √5625? =
20. 20.What is 90²? =
21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √1936? =
24. 24.A square garden has an area of 121 square m. How long is each side (in m)?
25. 25.What is 60²? =
26. 26.How many whole numbers lie between 9² and 10²?
27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
28. 28.A square garden has an area of 3600 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 38² and 39²?
30. 30.What is √4356? =
31. 31.What is √4225? =
32. 32.What is 16²? =
33. 33.Which of these is a perfect square? (a) 129 (b) 121 (c) 127
34. 34.What is 29²? =
35. 35.Which of these is a perfect square? (a) 435 (b) 400 (c) 405
36. 36.Which of these is a perfect square? (a) 194 (b) 183 (c) 169
37. 37.How many whole numbers lie between 8² and 9²?
38. 38.Which of these is a perfect square? (a) 529 (b) 539 (c) 531
39. 39.What is √324? =
40. 40.What is √225? =

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