Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 552 · 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 23² and 24²?
2. 2.Which of these is a perfect square? (a) 620 (b) 581 (c) 576
3. 3.What is √1849? =
4. 4.How many whole numbers lie between 10² and 11²?
5. 5.Which of these is a perfect square? (a) 147 (b) 150 (c) 144
6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 500 (b) 484 (c) 522
8. 8.Which of these is a perfect square? (a) 236 (b) 225 (c) 247
9. 9.Which of these is a perfect square? (a) 1013 (b) 961 (c) 966
10. 10.A square garden has an area of 144 square m. How long is each side (in m)?
11. 11.What is √961? =
12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 296 (b) 289 (c) 323
14. 14.What is the smallest whole number by which 18 must be divided to get a perfect square?
15. 15.What is 35²? =
16. 16.A square garden has an area of 841 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 40² and 41²?
18. 18.What is 82²? =
19. 19.What is √7056? =
20. 20.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
21. 21.How many whole numbers lie between 41² and 42²?
22. 22.What is the smallest whole number by which 63 must be divided to get a perfect square?
23. 23.What is 73²? =
24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 49² and 50²?
26. 26.Which of these is a perfect square? (a) 453 (b) 441 (c) 481
27. 27.What is the smallest whole number by which 52 must be divided to get a perfect square?
28. 28.A square garden has an area of 729 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 390 (b) 399 (c) 361
30. 30.How many whole numbers lie between 16² and 17²?
31. 31.What is 51²? =
32. 32.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
33. 33.How many whole numbers lie between 9² and 10²?
34. 34.What is 52²? =
35. 35.How many whole numbers lie between 35² and 36²?
36. 36.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √7569? =
39. 39.What is √625? =
40. 40.What is 12²? =

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