Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 142 · 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 √9801? =
2. 2.What is √6889? =
3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 34²? =
5. 5.A square garden has an area of 3136 square m. How long is each side (in m)?
6. 6.What is 54²? =
7. 7.Which of these is a perfect square? (a) 253 (b) 225 (c) 245
8. 8.What is 14²? =
9. 9.What is √8649? =
10. 10.A square garden has an area of 2304 square m. How long is each side (in m)?
11. 11.What is 73²? =
12. 12.A square garden has an area of 100 square m. How long is each side (in m)?
13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
14. 14.How many whole numbers lie between 24² and 25²?
15. 15.What is 59²? =
16. 16.Which of these is a perfect square? (a) 212 (b) 196 (c) 221
17. 17.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
18. 18.A square garden has an area of 2704 square m. How long is each side (in m)?
19. 19.A square garden has an area of 1444 square m. How long is each side (in m)?
20. 20.What is 32²? =
21. 21.What is √961? =
22. 22.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
23. 23.How many whole numbers lie between 15² and 16²?
24. 24.Which of these is a perfect square? (a) 934 (b) 900 (c) 954
25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √169? =
28. 28.How many whole numbers lie between 14² and 15²?
29. 29.Which of these is a perfect square? (a) 169 (b) 173 (c) 179
30. 30.What is the smallest whole number by which 1053 must be divided to get a perfect square?
31. 31.A square garden has an area of 1936 square m. How long is each side (in m)?
32. 32.What is 93²? =
33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 38² and 39²?
35. 35.What is √361? =
36. 36.Which of these is a perfect square? (a) 327 (b) 324 (c) 349
37. 37.What is √3136? =
38. 38.What is √1681? =
39. 39.How many whole numbers lie between 23² and 24²?
40. 40.A square garden has an area of 144 square m. How long is each side (in m)?

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