Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 332 · 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 sum of the first 12 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
3. 3.What is the smallest whole number by which 245 must be divided to get a perfect square?
4. 4.What is the smallest whole number by which 12 must be divided to get a perfect square?
5. 5.What is 46²? =
6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
8. 8.How many whole numbers lie between 44² and 45²?
9. 9.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
10. 10.What is √169? =
11. 11.What is 54²? =
12. 12.What is √361? =
13. 13.What is 64²? =
14. 14.How many whole numbers lie between 14² and 15²?
15. 15.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
16. 16.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
17. 17.A square garden has an area of 256 square m. How long is each side (in m)?
18. 18.What is √2500? =
19. 19.How many whole numbers lie between 45² and 46²?
20. 20.Which of these is a perfect square? (a) 1230 (b) 1225 (c) 1277
21. 21.How many whole numbers lie between 46² and 47²?
22. 22.What is √121? =
23. 23.How many whole numbers lie between 36² and 37²?
24. 24.A square garden has an area of 1521 square m. How long is each side (in m)?
25. 25.A square garden has an area of 100 square m. How long is each side (in m)?
26. 26.How many whole numbers lie between 21² and 22²?
27. 27.What is 78²? =
28. 28.How many whole numbers lie between 12² and 13²?
29. 29.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
30. 30.How many whole numbers lie between 26² and 27²?
31. 31.What is √2209? =
32. 32.What is √441? =
33. 33.A square garden has an area of 81 square m. How long is each side (in m)?
34. 34.A square garden has an area of 1156 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 491 (b) 484 (c) 493
36. 36.What is √1681? =
37. 37.How many whole numbers lie between 28² and 29²?
38. 38.What is 67²? =
39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 1936 square m. How long is each side (in m)?

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