Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 385 · 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 24²? =
2. 2.What is 59²? =
3. 3.How many whole numbers lie between 25² and 26²?
4. 4.What is √7225? =
5. 5.What is √6400? =
6. 6.What is √6561? =
7. 7.Which of these is a perfect square? (a) 289 (b) 300 (c) 316
8. 8.A square garden has an area of 576 square m. How long is each side (in m)?
9. 9.A square garden has an area of 529 square m. How long is each side (in m)?
10. 10.Which of these is a perfect square? (a) 441 (b) 450 (c) 456
11. 11.What is 84²? =
12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
14. 14.How many whole numbers lie between 33² and 34²?
15. 15.What is 36²? =
16. 16.What is √4624? =
17. 17.A square garden has an area of 441 square m. How long is each side (in m)?
18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
19. 19.A square garden has an area of 2116 square m. How long is each side (in m)?
20. 20.What is √5929? =
21. 21.How many whole numbers lie between 37² and 38²?
22. 22.How many whole numbers lie between 11² and 12²?
23. 23.How many whole numbers lie between 43² and 44²?
24. 24.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
25. 25.What is 88²? =
26. 26.A square garden has an area of 1156 square m. How long is each side (in m)?
27. 27.A square garden has an area of 2209 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
29. 29.How many whole numbers lie between 50² and 51²?
30. 30.How many whole numbers lie between 13² and 14²?
31. 31.A square garden has an area of 1444 square m. How long is each side (in m)?
32. 32.What is 12²? =
33. 33.What is the smallest whole number by which 1215 must be divided to get a perfect square?
34. 34.How many whole numbers lie between 10² and 11²?
35. 35.How many whole numbers lie between 29² and 30²?
36. 36.How many whole numbers lie between 28² and 29²?
37. 37.What is the smallest whole number by which 135 must be divided to get a perfect square?
38. 38.Which of these is a perfect square? (a) 1081 (b) 1044 (c) 1024
39. 39.What is 58²? =
40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?

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