Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 21 · 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 the smallest whole number by which 125 must be divided to get a perfect square?
2. 2.A square garden has an area of 1600 square m. How long is each side (in m)?
3. 3.How many whole numbers lie between 19² and 20²?
4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
6. 6.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 51²? =
9. 9.What is √4096? =
10. 10.What is √4225? =
11. 11.What is √1764? =
12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √1225? =
14. 14.What is √1849? =
15. 15.A square garden has an area of 121 square m. How long is each side (in m)?
16. 16.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
17. 17.Which of these is a perfect square? (a) 267 (b) 261 (c) 256
18. 18.Which of these is a perfect square? (a) 356 (b) 324 (c) 332
19. 19.What is √6561? =
20. 20.Which of these is a perfect square? (a) 1388 (b) 1405 (c) 1369
21. 21.What is √676? =
22. 22.What is √7921? =
23. 23.What is 14²? =
24. 24.What is √289? =
25. 25.What is √2401? =
26. 26.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
27. 27.How many whole numbers lie between 46² and 47²?
28. 28.How many whole numbers lie between 35² and 36²?
29. 29.Which of these is a perfect square? (a) 1080 (b) 1024 (c) 1031
30. 30.What is √3844? =
31. 31.What is 49²? =
32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
33. 33.How many whole numbers lie between 29² and 30²?
34. 34.How many whole numbers lie between 9² and 10²?
35. 35.What is √5476? =
36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √529? =
38. 38.How many whole numbers lie between 27² and 28²?
39. 39.A square garden has an area of 225 square m. How long is each side (in m)?
40. 40.How many whole numbers lie between 18² and 19²?

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