Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 688 · 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 3025 square m. How long is each side (in m)?
2. 2.What is 77²? =
3. 3.How many whole numbers lie between 30² and 31²?
4. 4.What is √5929? =
5. 5.How many whole numbers lie between 33² and 34²?
6. 6.What is √1296? =
7. 7.What is 39²? =
8. 8.What is 79²? =
9. 9.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
10. 10.What is √5776? =
11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 60²? =
13. 13.What is √676? =
14. 14.Which of these is a perfect square? (a) 1652 (b) 1600 (c) 1618
15. 15.What is 64²? =
16. 16.What is √2916? =
17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
18. 18.A square garden has an area of 2809 square m. How long is each side (in m)?
19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
21. 21.How many whole numbers lie between 27² and 28²?
22. 22.Which of these is a perfect square? (a) 108 (b) 100 (c) 114
23. 23.A square garden has an area of 196 square m. How long is each side (in m)?
24. 24.What is 26²? =
25. 25.How many whole numbers lie between 32² and 33²?
26. 26.What is √289? =
27. 27.What is 68²? =
28. 28.A square garden has an area of 2916 square m. How long is each side (in m)?
29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
30. 30.A square garden has an area of 144 square m. How long is each side (in m)?
31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √361? =
33. 33.How many whole numbers lie between 35² and 36²?
34. 34.What is 98²? =
35. 35.What is 33²? =
36. 36.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
37. 37.A square garden has an area of 2704 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 37² and 38²?
39. 39.What is √2601? =
40. 40.What is 80²? =

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