Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 242 · 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 49² and 50²?
2. 2.What is 25²? =
3. 3.What is 58²? =
4. 4.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
5. 5.A square garden has an area of 2809 square m. How long is each side (in m)?
6. 6.What is 37²? =
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
8. 8.How many whole numbers lie between 29² and 30²?
9. 9.How many whole numbers lie between 26² and 27²?
10. 10.What is √121? =
11. 11.What is √6400? =
12. 12.How many whole numbers lie between 48² and 49²?
13. 13.What is √1225? =
14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 89²? =
16. 16.What is 66²? =
17. 17.What is √4489? =
18. 18.How many whole numbers lie between 14² and 15²?
19. 19.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
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 20 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 42²? =
24. 24.How many whole numbers lie between 16² and 17²?
25. 25.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
26. 26.What is √8649? =
27. 27.How many whole numbers lie between 23² and 24²?
28. 28.What is √225? =
29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
30. 30.How many whole numbers lie between 44² and 45²?
31. 31.How many whole numbers lie between 46² and 47²?
32. 32.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
33. 33.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 31²? =
37. 37.A square garden has an area of 1089 square m. How long is each side (in m)?
38. 38.What is √4096? =
39. 39.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 324 square m. How long is each side (in m)?

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