Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 68 · 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 7² and 8²?
2. 2.What is 23²? =
3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √6400? =
5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
6. 6.Which of these is a perfect square? (a) 1581 (b) 1591 (c) 1521
7. 7.What is 68²? =
8. 8.What is 67²? =
9. 9.What is 21²? =
10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 1764 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 841 square m. How long is each side (in m)?
14. 14.A square garden has an area of 2601 square m. How long is each side (in m)?
15. 15.What is the smallest whole number by which 240 must be divided to get a perfect square?
16. 16.How many whole numbers lie between 43² and 44²?
17. 17.What is the smallest whole number by which 18 must be divided to get a perfect square?
18. 18.How many whole numbers lie between 22² and 23²?
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 756 (b) 747 (c) 729
21. 21.What is 53²? =
22. 22.Which of these is a perfect square? (a) 961 (b) 1017 (c) 984
23. 23.What is √9025? =
24. 24.How many whole numbers lie between 15² and 16²?
25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √900? =
28. 28.What is 88²? =
29. 29.What is 60²? =
30. 30.A square garden has an area of 2209 square m. How long is each side (in m)?
31. 31.What is √529? =
32. 32.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
33. 33.Which of these is a perfect square? (a) 1444 (b) 1493 (c) 1458
34. 34.Which of these is a perfect square? (a) 225 (b) 231 (c) 232
35. 35.What is 38²? =
36. 36.What is 69²? =
37. 37.What is 34²? =
38. 38.What is √289? =
39. 39.How many whole numbers lie between 27² and 28²?
40. 40.How many whole numbers lie between 18² and 19²?

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