Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 122 · 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 1764 square m. How long is each side (in m)?
2. 2.What is 59²? =
3. 3.What is 56²? =
4. 4.Which of these is a perfect square? (a) 127 (b) 121 (c) 143
5. 5.How many whole numbers lie between 43² and 44²?
6. 6.Which of these is a perfect square? (a) 433 (b) 436 (c) 400
7. 7.What is 98²? =
8. 8.What is 66²? =
9. 9.Which of these is a perfect square? (a) 1296 (b) 1321 (c) 1316
10. 10.How many whole numbers lie between 38² and 39²?
11. 11.What is 15²? =
12. 12.How many whole numbers lie between 29² and 30²?
13. 13.What is √7056? =
14. 14.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
15. 15.What is √5929? =
16. 16.What is 25²? =
17. 17.What is √225? =
18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 103 (b) 102 (c) 100
20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 46²? =
22. 22.What is 79²? =
23. 23.A square garden has an area of 49 square m. How long is each side (in m)?
24. 24.What is 42²? =
25. 25.Which of these is a perfect square? (a) 289 (b) 321 (c) 295
26. 26.Which of these is a perfect square? (a) 1290 (b) 1275 (c) 1225
27. 27.What is the smallest whole number by which 20 must be divided to get a perfect square?
28. 28.What is √1089? =
29. 29.Which of these is a perfect square? (a) 1168 (b) 1156 (c) 1162
30. 30.What is the smallest whole number by which 90 must be divided to get a perfect square?
31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 764 (b) 752 (c) 729
33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √1600? =
36. 36.A square garden has an area of 2116 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
38. 38.Which of these is a perfect square? (a) 285 (b) 256 (c) 269
39. 39.A square garden has an area of 441 square m. How long is each side (in m)?
40. 40.A square garden has an area of 841 square m. How long is each side (in m)?

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