Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 271 · 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 196 square m. How long is each side (in m)?
2. 2.What is 19²? =
3. 3.A square garden has an area of 64 square m. How long is each side (in m)?
4. 4.What is 42²? =
5. 5.What is √2704? =
6. 6.What is the smallest whole number by which 275 must be divided to get a perfect square?
7. 7.What is 17²? =
8. 8.Which of these is a perfect square? (a) 121 (b) 130 (c) 133
9. 9.What is 13²? =
10. 10.A square garden has an area of 2025 square m. How long is each side (in m)?
11. 11.What is 95²? =
12. 12.What is 77²? =
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 216 must be divided to get a perfect square?
16. 16.Which of these is a perfect square? (a) 362 (b) 361 (c) 368
17. 17.What is √3136? =
18. 18.Which of these is a perfect square? (a) 975 (b) 971 (c) 961
19. 19.What is 53²? =
20. 20.How many whole numbers lie between 16² and 17²?
21. 21.How many whole numbers lie between 26² and 27²?
22. 22.A square garden has an area of 256 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 179 (b) 169 (c) 186
24. 24.Which of these is a perfect square? (a) 1129 (b) 1150 (c) 1089
25. 25.What is the smallest whole number by which 98 must be divided to get a perfect square?
26. 26.What is √1369? =
27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √625? =
29. 29.What is the smallest whole number by which 208 must be divided to get a perfect square?
30. 30.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
31. 31.How many whole numbers lie between 46² and 47²?
32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √1936? =
34. 34.Which of these is a perfect square? (a) 784 (b) 829 (c) 794
35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 2916 square m. How long is each side (in m)?
37. 37.What is √676? =
38. 38.What is √2916? =
39. 39.How many whole numbers lie between 44² and 45²?
40. 40.What is 43²? =

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