Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 604 · 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 √1225? =
2. 2.What is the smallest whole number by which 490 must be divided to get a perfect square?
3. 3.What is 51²? =
4. 4.What is √4356? =
5. 5.How many whole numbers lie between 9² and 10²?
6. 6.A square garden has an area of 81 square m. How long is each side (in m)?
7. 7.A square garden has an area of 2704 square m. How long is each side (in m)?
8. 8.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
9. 9.Which of these is a perfect square? (a) 169 (b) 190 (c) 177
10. 10.How many whole numbers lie between 14² and 15²?
11. 11.Which of these is a perfect square? (a) 129 (b) 121 (c) 126
12. 12.Which of these is a perfect square? (a) 568 (b) 529 (c) 572
13. 13.What is √7056? =
14. 14.What is √9025? =
15. 15.What is the smallest whole number by which 99 must be divided to get a perfect square?
16. 16.How many whole numbers lie between 23² and 24²?
17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √1764? =
19. 19.What is the smallest whole number by which 275 must be divided to get a perfect square?
20. 20.What is the smallest whole number by which 180 must be divided to get a perfect square?
21. 21.Which of these is a perfect square? (a) 1156 (b) 1168 (c) 1171
22. 22.What is √625? =
23. 23.A square garden has an area of 100 square m. How long is each side (in m)?
24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √576? =
29. 29.A square garden has an area of 361 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 18² and 19²?
31. 31.Which of these is a perfect square? (a) 1397 (b) 1419 (c) 1369
32. 32.What is 90²? =
33. 33.What is 54²? =
34. 34.How many whole numbers lie between 8² and 9²?
35. 35.What is 53²? =
36. 36.A square garden has an area of 25 square m. How long is each side (in m)?
37. 37.A square garden has an area of 1024 square m. How long is each side (in m)?
38. 38.Which of these is a perfect square? (a) 291 (b) 294 (c) 289
39. 39.What is 73²? =
40. 40.A square garden has an area of 169 square m. How long is each side (in m)?

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