Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 213 · 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) 690 (b) 676 (c) 677
2. 2.A square garden has an area of 1681 square m. How long is each side (in m)?
3. 3.What is √289? =
4. 4.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
5. 5.What is √9216? =
6. 6.What is 29²? =
7. 7.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
8. 8.How many whole numbers lie between 45² and 46²?
9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
11. 11.How many whole numbers lie between 6² and 7²?
12. 12.Which of these is a perfect square? (a) 1156 (b) 1223 (c) 1176
13. 13.A square garden has an area of 3364 square m. How long is each side (in m)?
14. 14.A square garden has an area of 1600 square m. How long is each side (in m)?
15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
16. 16.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
17. 17.What is 90²? =
18. 18.A square garden has an area of 196 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 32 must be divided to get a perfect square?
20. 20.What is 84²? =
21. 21.A square garden has an area of 81 square m. How long is each side (in m)?
22. 22.How many whole numbers lie between 28² and 29²?
23. 23.What is √6889? =
24. 24.How many whole numbers lie between 46² and 47²?
25. 25.What is √7744? =
26. 26.What is 57²? =
27. 27.How many whole numbers lie between 29² and 30²?
28. 28.How many whole numbers lie between 21² and 22²?
29. 29.What is √7569? =
30. 30.What is √6561? =
31. 31.How many whole numbers lie between 34² and 35²?
32. 32.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
33. 33.What is 19²? =
34. 34.What is 49²? =
35. 35.What is √529? =
36. 36.A square garden has an area of 676 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
38. 38.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
39. 39.A square garden has an area of 2916 square m. How long is each side (in m)?
40. 40.What is 97²? =

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