Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 150 · 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 896 must be divided to get a perfect square?
2. 2.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
3. 3.How many whole numbers lie between 16² and 17²?
4. 4.What is 30²? =
5. 5.A square garden has an area of 1444 square m. How long is each side (in m)?
6. 6.What is √7921? =
7. 7.Which of these is a perfect square? (a) 583 (b) 609 (c) 576
8. 8.A square garden has an area of 3364 square m. How long is each side (in m)?
9. 9.Which of these is a perfect square? (a) 729 (b) 738 (c) 763
10. 10.What is 92²? =
11. 11.What is 56²? =
12. 12.How many whole numbers lie between 34² and 35²?
13. 13.What is the smallest whole number by which 180 must be divided to get a perfect square?
14. 14.Which of these is a perfect square? (a) 144 (b) 151 (c) 150
15. 15.What is 27²? =
16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
18. 18.A square garden has an area of 1369 square m. How long is each side (in m)?
19. 19.How many whole numbers lie between 18² and 19²?
20. 20.Which of these is a perfect square? (a) 131 (b) 128 (c) 121
21. 21.What is √3600? =
22. 22.A square garden has an area of 1296 square m. How long is each side (in m)?
23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
24. 24.A square garden has an area of 3025 square m. How long is each side (in m)?
25. 25.What is 40²? =
26. 26.Which of these is a perfect square? (a) 1639 (b) 1600 (c) 1632
27. 27.Which of these is a perfect square? (a) 943 (b) 921 (c) 900
28. 28.How many whole numbers lie between 19² and 20²?
29. 29.What is √324? =
30. 30.What is √1089? =
31. 31.How many whole numbers lie between 50² and 51²?
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √5041? =
34. 34.What is √196? =
35. 35.A square garden has an area of 256 square m. How long is each side (in m)?
36. 36.A square garden has an area of 2304 square m. How long is each side (in m)?
37. 37.What is 68²? =
38. 38.Which of these is a perfect square? (a) 326 (b) 359 (c) 324
39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 196 square m. How long is each side (in m)?

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