Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 138 · 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 8 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 18 must be divided to get a perfect square?
3. 3.A square garden has an area of 2304 square m. How long is each side (in m)?
4. 4.What is 34²? =
5. 5.How many whole numbers lie between 50² and 51²?
6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
8. 8.What is √289? =
9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
10. 10.How many whole numbers lie between 24² and 25²?
11. 11.Which of these is a perfect square? (a) 676 (b) 698 (c) 697
12. 12.How many whole numbers lie between 34² and 35²?
13. 13.What is 52²? =
14. 14.How many whole numbers lie between 49² and 50²?
15. 15.Which of these is a perfect square? (a) 249 (b) 246 (c) 225
16. 16.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 14² and 15²?
19. 19.A square garden has an area of 2601 square m. How long is each side (in m)?
20. 20.What is √3136? =
21. 21.What is 90²? =
22. 22.How many whole numbers lie between 29² and 30²?
23. 23.Which of these is a perfect square? (a) 264 (b) 256 (c) 283
24. 24.What is √361? =
25. 25.How many whole numbers lie between 35² and 36²?
26. 26.What is √7569? =
27. 27.What is 65²? =
28. 28.Which of these is a perfect square? (a) 500 (b) 521 (c) 484
29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √625? =
31. 31.What is √1849? =
32. 32.How many whole numbers lie between 37² and 38²?
33. 33.A square garden has an area of 64 square m. How long is each side (in m)?
34. 34.What is √576? =
35. 35.How many whole numbers lie between 36² and 37²?
36. 36.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
37. 37.What is 94²? =
38. 38.A square garden has an area of 729 square m. How long is each side (in m)?
39. 39.What is √1444? =
40. 40.What is 32²? =

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