Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 325 · 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 the smallest whole number by which 252 must be divided to get a perfect square?
2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 31²? =
5. 5.What is 58²? =
6. 6.How many whole numbers lie between 34² and 35²?
7. 7.What is 19²? =
8. 8.What is √3136? =
9. 9.A square garden has an area of 1089 square m. How long is each side (in m)?
10. 10.Which of these is a perfect square? (a) 790 (b) 784 (c) 804
11. 11.How many whole numbers lie between 29² and 30²?
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
14. 14.What is 81²? =
15. 15.What is √4225? =
16. 16.A square garden has an area of 2401 square m. How long is each side (in m)?
17. 17.What is √400? =
18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 18²? =
20. 20.Which of these is a perfect square? (a) 694 (b) 709 (c) 676
21. 21.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
23. 23.What is √4489? =
24. 24.What is √3364? =
25. 25.What is the smallest whole number by which 360 must be divided to get a perfect square?
26. 26.Which of these is a perfect square? (a) 900 (b) 950 (c) 920
27. 27.What is √4761? =
28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
30. 30.What is 24²? =
31. 31.What is √1849? =
32. 32.How many whole numbers lie between 22² and 23²?
33. 33.Which of these is a perfect square? (a) 1107 (b) 1089 (c) 1108
34. 34.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
35. 35.How many whole numbers lie between 18² and 19²?
36. 36.How many whole numbers lie between 26² and 27²?
37. 37.How many whole numbers lie between 27² and 28²?
38. 38.What is 60²? =
39. 39.A square garden has an area of 36 square m. How long is each side (in m)?
40. 40.What is 75²? =

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