Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 468 · 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.A square garden has an area of 484 square m. How long is each side (in m)?
2. 2.A square garden has an area of 324 square m. How long is each side (in m)?
3. 3.A square garden has an area of 2601 square m. How long is each side (in m)?
4. 4.What is the smallest whole number by which 275 must be divided to get a perfect square?
5. 5.What is √6241? =
6. 6.Which of these is a perfect square? (a) 121 (b) 127 (c) 138
7. 7.What is 83²? =
8. 8.What is 39²? =
9. 9.How many whole numbers lie between 31² and 32²?
10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √1681? =
12. 12.A square garden has an area of 3025 square m. How long is each side (in m)?
13. 13.A square garden has an area of 196 square m. How long is each side (in m)?
14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
15. 15.A square garden has an area of 36 square m. How long is each side (in m)?
16. 16.A square garden has an area of 676 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 12² and 13²?
18. 18.What is √3600? =
19. 19.How many whole numbers lie between 23² and 24²?
20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
23. 23.How many whole numbers lie between 25² and 26²?
24. 24.How many whole numbers lie between 14² and 15²?
25. 25.How many whole numbers lie between 44² and 45²?
26. 26.What is √625? =
27. 27.What is 27²? =
28. 28.What is 89²? =
29. 29.What is the smallest whole number by which 50 must be divided to get a perfect square?
30. 30.What is √144? =
31. 31.How many whole numbers lie between 39² and 40²?
32. 32.Which of these is a perfect square? (a) 1677 (b) 1600 (c) 1618
33. 33.What is 68²? =
34. 34.What is the smallest whole number by which 891 must be divided to get a perfect square?
35. 35.What is √1369? =
36. 36.Which of these is a perfect square? (a) 368 (b) 369 (c) 361
37. 37.What is √841? =
38. 38.What is √121? =
39. 39.Which of these is a perfect square? (a) 961 (b) 994 (c) 1023
40. 40.What is √784? =

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