Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 702 · 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 29²? =
2. 2.What is the smallest whole number by which 448 must be divided to get a perfect square?
3. 3.How many whole numbers lie between 24² and 25²?
4. 4.Which of these is a perfect square? (a) 729 (b) 750 (c) 731
5. 5.Which of these is a perfect square? (a) 217 (b) 196 (c) 205
6. 6.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
7. 7.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
9. 9.A square garden has an area of 256 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 192 must be divided to get a perfect square?
11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 47²? =
13. 13.What is 63²? =
14. 14.What is 98²? =
15. 15.What is √225? =
16. 16.What is √4900? =
17. 17.Which of these is a perfect square? (a) 715 (b) 709 (c) 676
18. 18.What is √1089? =
19. 19.What is 68²? =
20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
23. 23.What is 27²? =
24. 24.What is 74²? =
25. 25.Which of these is a perfect square? (a) 324 (b) 356 (c) 329
26. 26.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
27. 27.How many whole numbers lie between 43² and 44²?
28. 28.How many whole numbers lie between 46² and 47²?
29. 29.How many whole numbers lie between 11² and 12²?
30. 30.What is 39²? =
31. 31.What is √5929? =
32. 32.What is √361? =
33. 33.Which of these is a perfect square? (a) 118 (b) 100 (c) 101
34. 34.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
35. 35.What is 62²? =
36. 36.What is 16²? =
37. 37.What is 90²? =
38. 38.Which of these is a perfect square? (a) 900 (b) 934 (c) 944
39. 39.What is 38²? =
40. 40.What is 99²? =

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