Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 551 · 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 58²? =
2. 2.Which of these is a perfect square? (a) 1137 (b) 1089 (c) 1104
3. 3.What is 92²? =
4. 4.What is √5041? =
5. 5.Which of these is a perfect square? (a) 387 (b) 394 (c) 361
6. 6.What is 48²? =
7. 7.How many whole numbers lie between 13² and 14²?
8. 8.How many whole numbers lie between 30² and 31²?
9. 9.What is 64²? =
10. 10.What is √729? =
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 1600 (b) 1624 (c) 1611
13. 13.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
14. 14.Which of these is a perfect square? (a) 627 (b) 654 (c) 625
15. 15.What is √1444? =
16. 16.How many whole numbers lie between 40² and 41²?
17. 17.How many whole numbers lie between 42² and 43²?
18. 18.How many whole numbers lie between 12² and 13²?
19. 19.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
20. 20.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
21. 21.How many whole numbers lie between 27² and 28²?
22. 22.A square garden has an area of 961 square m. How long is each side (in m)?
23. 23.What is √6241? =
24. 24.What is √7056? =
25. 25.How many whole numbers lie between 24² and 25²?
26. 26.A square garden has an area of 2025 square m. How long is each side (in m)?
27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
29. 29.How many whole numbers lie between 50² and 51²?
30. 30.A square garden has an area of 1024 square m. How long is each side (in m)?
31. 31.What is √1849? =
32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √4489? =
34. 34.A square garden has an area of 144 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 9² and 10²?
36. 36.Which of these is a perfect square? (a) 1012 (b) 961 (c) 969
37. 37.A square garden has an area of 1849 square m. How long is each side (in m)?
38. 38.A square garden has an area of 1936 square m. How long is each side (in m)?
39. 39.What is 14²? =
40. 40.How many whole numbers lie between 44² and 45²?

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