Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 541 · 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 59²? =
2. 2.What is √9025? =
3. 3.How many whole numbers lie between 13² and 14²?
4. 4.Which of these is a perfect square? (a) 874 (b) 841 (c) 883
5. 5.What is √8836? =
6. 6.Which of these is a perfect square? (a) 296 (b) 315 (c) 289
7. 7.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
8. 8.What is 16²? =
9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
10. 10.How many whole numbers lie between 8² and 9²?
11. 11.What is 27²? =
12. 12.How many whole numbers lie between 9² and 10²?
13. 13.Which of these is a perfect square? (a) 163 (b) 168 (c) 144
14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 350 must be divided to get a perfect square?
16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
17. 17.Which of these is a perfect square? (a) 225 (b) 244 (c) 236
18. 18.What is √7056? =
19. 19.What is √1089? =
20. 20.Which of these is a perfect square? (a) 1625 (b) 1600 (c) 1636
21. 21.What is 20²? =
22. 22.How many whole numbers lie between 50² and 51²?
23. 23.How many whole numbers lie between 32² and 33²?
24. 24.Which of these is a perfect square? (a) 1296 (b) 1316 (c) 1306
25. 25.What is √289? =
26. 26.What is √1681? =
27. 27.Which of these is a perfect square? (a) 545 (b) 529 (c) 534
28. 28.What is 62²? =
29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 576 (b) 616 (c) 589
31. 31.What is 19²? =
32. 32.What is the smallest whole number by which 294 must be divided to get a perfect square?
33. 33.What is √841? =
34. 34.How many whole numbers lie between 43² and 44²?
35. 35.How many whole numbers lie between 33² and 34²?
36. 36.How many whole numbers lie between 48² and 49²?
37. 37.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
38. 38.Which of these is a perfect square? (a) 425 (b) 400 (c) 426
39. 39.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
40. 40.What is 75²? =

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