Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 436 · 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.How many whole numbers lie between 16² and 17²?
2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
3. 3.A square garden has an area of 1369 square m. How long is each side (in m)?
4. 4.What is 46²? =
5. 5.A square garden has an area of 1681 square m. How long is each side (in m)?
6. 6.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
7. 7.A square garden has an area of 324 square m. How long is each side (in m)?
8. 8.What is √900? =
9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 96²? =
12. 12.Which of these is a perfect square? (a) 601 (b) 579 (c) 576
13. 13.How many whole numbers lie between 31² and 32²?
14. 14.What is √1521? =
15. 15.Which of these is a perfect square? (a) 639 (b) 625 (c) 628
16. 16.What is 56²? =
17. 17.How many whole numbers lie between 42² and 43²?
18. 18.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
19. 19.A square garden has an area of 121 square m. How long is each side (in m)?
20. 20.What is 72²? =
21. 21.What is √6241? =
22. 22.What is 26²? =
23. 23.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
24. 24.How many whole numbers lie between 7² and 8²?
25. 25.A square garden has an area of 2601 square m. How long is each side (in m)?
26. 26.How many whole numbers lie between 23² and 24²?
27. 27.What is 77²? =
28. 28.A square garden has an area of 676 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 27² and 28²?
30. 30.How many whole numbers lie between 40² and 41²?
31. 31.What is √1369? =
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √169? =
34. 34.How many whole numbers lie between 41² and 42²?
35. 35.Which of these is a perfect square? (a) 1089 (b) 1125 (c) 1101
36. 36.Which of these is a perfect square? (a) 235 (b) 225 (c) 237
37. 37.What is the smallest whole number by which 150 must be divided to get a perfect square?
38. 38.What is 13²? =
39. 39.What is the smallest whole number by which 24 must be divided to get a perfect square?
40. 40.What is √289? =

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