Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 299 · 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 70²? =
2. 2.How many whole numbers lie between 38² and 39²?
3. 3.What is 83²? =
4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 22² and 23²?
6. 6.How many whole numbers lie between 5² and 6²?
7. 7.Which of these is a perfect square? (a) 1549 (b) 1522 (c) 1521
8. 8.What is √6561? =
9. 9.How many whole numbers lie between 20² and 21²?
10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 33²? =
12. 12.A square garden has an area of 1681 square m. How long is each side (in m)?
13. 13.How many whole numbers lie between 39² and 40²?
14. 14.How many whole numbers lie between 37² and 38²?
15. 15.How many whole numbers lie between 10² and 11²?
16. 16.How many whole numbers lie between 18² and 19²?
17. 17.Which of these is a perfect square? (a) 1096 (b) 1155 (c) 1089
18. 18.How many whole numbers lie between 46² and 47²?
19. 19.What is √900? =
20. 20.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
21. 21.What is 76²? =
22. 22.Which of these is a perfect square? (a) 1024 (b) 1025 (c) 1067
23. 23.Which of these is a perfect square? (a) 289 (b) 305 (c) 298
24. 24.What is √3844? =
25. 25.What is √7921? =
26. 26.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
27. 27.How many whole numbers lie between 35² and 36²?
28. 28.What is √1444? =
29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 743 (b) 729 (c) 759
31. 31.What is 97²? =
32. 32.A square garden has an area of 324 square m. How long is each side (in m)?
33. 33.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
34. 34.What is √1024? =
35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 18²? =
37. 37.Which of these is a perfect square? (a) 489 (b) 526 (c) 484
38. 38.Which of these is a perfect square? (a) 814 (b) 829 (c) 784
39. 39.How many whole numbers lie between 24² and 25²?
40. 40.How many whole numbers lie between 8² and 9²?

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