Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 218 · 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.How many whole numbers lie between 50² and 51²?
2. 2.How many whole numbers lie between 21² and 22²?
3. 3.What is 97²? =
4. 4.What is 40²? =
5. 5.A square garden has an area of 900 square m. How long is each side (in m)?
6. 6.How many whole numbers lie between 6² and 7²?
7. 7.Which of these is a perfect square? (a) 726 (b) 676 (c) 688
8. 8.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 832 must be divided to get a perfect square?
11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
13. 13.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
14. 14.What is 37²? =
15. 15.What is the smallest whole number by which 27 must be divided to get a perfect square?
16. 16.How many whole numbers lie between 12² and 13²?
17. 17.A square garden has an area of 784 square m. How long is each side (in m)?
18. 18.What is the smallest whole number by which 567 must be divided to get a perfect square?
19. 19.What is 53²? =
20. 20.What is √324? =
21. 21.A square garden has an area of 49 square m. How long is each side (in m)?
22. 22.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
23. 23.What is 72²? =
24. 24.A square garden has an area of 81 square m. How long is each side (in m)?
25. 25.A square garden has an area of 1681 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 208 must be divided to get a perfect square?
27. 27.How many whole numbers lie between 30² and 31²?
28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
29. 29.What is √900? =
30. 30.What is 63²? =
31. 31.A square garden has an area of 3249 square m. How long is each side (in m)?
32. 32.What is √8100? =
33. 33.A square garden has an area of 2304 square m. How long is each side (in m)?
34. 34.A square garden has an area of 1600 square m. How long is each side (in m)?
35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √7569? =
38. 38.What is 54²? =
39. 39.What is the smallest whole number by which 48 must be divided to get a perfect square?
40. 40.What is √9801? =

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