Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 135 · 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.Which of these is a perfect square? (a) 178 (b) 169 (c) 183
2. 2.How many whole numbers lie between 30² and 31²?
3. 3.How many whole numbers lie between 27² and 28²?
4. 4.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 289 square m. How long is each side (in m)?
6. 6.A square garden has an area of 100 square m. How long is each side (in m)?
7. 7.Which of these is a perfect square? (a) 287 (b) 265 (c) 256
8. 8.What is √1369? =
9. 9.Which of these is a perfect square? (a) 379 (b) 361 (c) 395
10. 10.Which of these is a perfect square? (a) 156 (b) 144 (c) 157
11. 11.What is √3364? =
12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √1681? =
14. 14.What is 60²? =
15. 15.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
16. 16.How many whole numbers lie between 13² and 14²?
17. 17.What is 61²? =
18. 18.How many whole numbers lie between 34² and 35²?
19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
20. 20.How many whole numbers lie between 5² and 6²?
21. 21.A square garden has an area of 25 square m. How long is each side (in m)?
22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
24. 24.How many whole numbers lie between 10² and 11²?
25. 25.What is the smallest whole number by which 1215 must be divided to get a perfect square?
26. 26.What is 28²? =
27. 27.What is 86²? =
28. 28.What is the smallest whole number by which 20 must be divided to get a perfect square?
29. 29.What is 31²? =
30. 30.What is the smallest whole number by which 1053 must be divided to get a perfect square?
31. 31.Which of these is a perfect square? (a) 706 (b) 676 (c) 705
32. 32.Which of these is a perfect square? (a) 136 (b) 121 (c) 143
33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 529 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 11² and 12²?
36. 36.How many whole numbers lie between 12² and 13²?
37. 37.What is √3249? =
38. 38.How many whole numbers lie between 35² and 36²?
39. 39.What is √8464? =
40. 40.What is 48²? =

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