Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 461 · 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 the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
3. 3.What is √729? =
4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 37² and 38²?
6. 6.What is 24²? =
7. 7.Which of these is a perfect square? (a) 676 (b) 688 (c) 691
8. 8.What is √6724? =
9. 9.What is 60²? =
10. 10.How many whole numbers lie between 15² and 16²?
11. 11.What is 87²? =
12. 12.A square garden has an area of 1764 square m. How long is each side (in m)?
13. 13.A square garden has an area of 225 square m. How long is each side (in m)?
14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 99²? =
16. 16.What is 68²? =
17. 17.What is √8836? =
18. 18.What is 22²? =
19. 19.What is √3249? =
20. 20.How many whole numbers lie between 16² and 17²?
21. 21.What is 74²? =
22. 22.A square garden has an area of 1444 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 1590 (b) 1521 (c) 1538
24. 24.Which of these is a perfect square? (a) 127 (b) 132 (c) 121
25. 25.A square garden has an area of 2916 square m. How long is each side (in m)?
26. 26.What is √5041? =
27. 27.What is the smallest whole number by which 735 must be divided to get a perfect square?
28. 28.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
29. 29.What is 18²? =
30. 30.What is √2401? =
31. 31.Which of these is a perfect square? (a) 225 (b) 231 (c) 249
32. 32.How many whole numbers lie between 34² and 35²?
33. 33.What is √2209? =
34. 34.What is √361? =
35. 35.What is 80²? =
36. 36.What is √676? =
37. 37.How many whole numbers lie between 46² and 47²?
38. 38.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √4624? =
40. 40.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?

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