Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 80 · 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 46²? =
2. 2.Which of these is a perfect square? (a) 1434 (b) 1438 (c) 1369
3. 3.A square garden has an area of 484 square m. How long is each side (in m)?
4. 4.What is √841? =
5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √3600? =
9. 9.A square garden has an area of 324 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
11. 11.How many whole numbers lie between 33² and 34²?
12. 12.What is √2704? =
13. 13.What is 31²? =
14. 14.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
15. 15.What is 86²? =
16. 16.A square garden has an area of 841 square m. How long is each side (in m)?
17. 17.What is 37²? =
18. 18.A square garden has an area of 3025 square m. How long is each side (in m)?
19. 19.How many whole numbers lie between 43² and 44²?
20. 20.Which of these is a perfect square? (a) 362 (b) 361 (c) 399
21. 21.What is √8464? =
22. 22.A square garden has an area of 3249 square m. How long is each side (in m)?
23. 23.What is 43²? =
24. 24.How many whole numbers lie between 27² and 28²?
25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
26. 26.A square garden has an area of 1156 square m. How long is each side (in m)?
27. 27.What is 87²? =
28. 28.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
29. 29.A square garden has an area of 2209 square m. How long is each side (in m)?
30. 30.What is √5476? =
31. 31.How many whole numbers lie between 39² and 40²?
32. 32.What is √8281? =
33. 33.What is √196? =
34. 34.What is 35²? =
35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 30²? =
37. 37.How many whole numbers lie between 21² and 22²?
38. 38.How many whole numbers lie between 18² and 19²?
39. 39.What is √169? =
40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?

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