Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 83 · 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) 576 (b) 620 (c) 591
2. 2.What is 56²? =
3. 3.Which of these is a perfect square? (a) 1082 (b) 1024 (c) 1042
4. 4.What is √9025? =
5. 5.What is 15²? =
6. 6.What is the smallest whole number by which 637 must be divided to get a perfect square?
7. 7.What is 83²? =
8. 8.What is 23²? =
9. 9.How many whole numbers lie between 23² and 24²?
10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
11. 11.How many whole numbers lie between 49² and 50²?
12. 12.What is 13²? =
13. 13.What is 41²? =
14. 14.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
15. 15.A square garden has an area of 1681 square m. How long is each side (in m)?
16. 16.What is the smallest whole number by which 18 must be divided to get a perfect square?
17. 17.What is √1600? =
18. 18.What is √8649? =
19. 19.A square garden has an area of 961 square m. How long is each side (in m)?
20. 20.What is √7396? =
21. 21.A square garden has an area of 64 square m. How long is each side (in m)?
22. 22.What is 96²? =
23. 23.What is √1444? =
24. 24.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √4096? =
26. 26.How many whole numbers lie between 35² and 36²?
27. 27.What is 22²? =
28. 28.How many whole numbers lie between 34² and 35²?
29. 29.What is 35²? =
30. 30.How many whole numbers lie between 10² and 11²?
31. 31.What is √6724? =
32. 32.Which of these is a perfect square? (a) 144 (b) 150 (c) 148
33. 33.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
34. 34.How many whole numbers lie between 14² and 15²?
35. 35.What is √576? =
36. 36.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
37. 37.Which of these is a perfect square? (a) 1427 (b) 1371 (c) 1369
38. 38.What is 65²? =
39. 39.Which of these is a perfect square? (a) 315 (b) 289 (c) 295
40. 40.What is 88²? =

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