Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 355 · 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 49²? =
2. 2.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
4. 4.How many whole numbers lie between 33² and 34²?
5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 24²? =
7. 7.What is 58²? =
8. 8.What is 25²? =
9. 9.How many whole numbers lie between 7² and 8²?
10. 10.What is 91²? =
11. 11.How many whole numbers lie between 38² and 39²?
12. 12.How many whole numbers lie between 19² and 20²?
13. 13.Which of these is a perfect square? (a) 1354 (b) 1316 (c) 1296
14. 14.Which of these is a perfect square? (a) 565 (b) 534 (c) 529
15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 634 (b) 625 (c) 671
17. 17.How many whole numbers lie between 25² and 26²?
18. 18.What is √3600? =
19. 19.How many whole numbers lie between 21² and 22²?
20. 20.What is √2601? =
21. 21.Which of these is a perfect square? (a) 1158 (b) 1156 (c) 1185
22. 22.What is √841? =
23. 23.What is 32²? =
24. 24.What is √8100? =
25. 25.What is the smallest whole number by which 396 must be divided to get a perfect square?
26. 26.A square garden has an area of 2401 square m. How long is each side (in m)?
27. 27.A square garden has an area of 196 square m. How long is each side (in m)?
28. 28.What is 74²? =
29. 29.A square garden has an area of 1681 square m. How long is each side (in m)?
30. 30.What is √3249? =
31. 31.A square garden has an area of 784 square m. How long is each side (in m)?
32. 32.What is √529? =
33. 33.How many whole numbers lie between 28² and 29²?
34. 34.A square garden has an area of 81 square m. How long is each side (in m)?
35. 35.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
36. 36.How many whole numbers lie between 41² and 42²?
37. 37.A square garden has an area of 441 square m. How long is each side (in m)?
38. 38.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
39. 39.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
40. 40.What is √121? =

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