Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 629 · 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) 1101 (b) 1124 (c) 1089
2. 2.What is 34²? =
3. 3.What is √4624? =
4. 4.Which of these is a perfect square? (a) 435 (b) 412 (c) 400
5. 5.What is the smallest whole number by which 640 must be multiplied to get a perfect square?
6. 6.What is the smallest whole number by which 40 must be divided to get a perfect square?
7. 7.What is √5625? =
8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
9. 9.What is √8100? =
10. 10.A square garden has an area of 324 square m. How long is each side (in m)?
11. 11.What is 63²? =
12. 12.A square garden has an area of 784 square m. How long is each side (in m)?
13. 13.What is 99²? =
14. 14.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
17. 17.How many whole numbers lie between 38² and 39²?
18. 18.How many whole numbers lie between 30² and 31²?
19. 19.What is 89²? =
20. 20.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
22. 22.What is 72²? =
23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
25. 25.Which of these is a perfect square? (a) 173 (b) 169 (c) 181
26. 26.What is √400? =
27. 27.What is the smallest whole number by which 8 must be divided to get a perfect square?
28. 28.Which of these is a perfect square? (a) 222 (b) 200 (c) 196
29. 29.What is √784? =
30. 30.Which of these is a perfect square? (a) 650 (b) 625 (c) 652
31. 31.How many whole numbers lie between 34² and 35²?
32. 32.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
33. 33.What is √8464? =
34. 34.What is √3721? =
35. 35.How many whole numbers lie between 36² and 37²?
36. 36.What is 40²? =
37. 37.A square garden has an area of 225 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 26² and 27²?
39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
40. 40.What is √6724? =

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