Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 506 · 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 36 square m. How long is each side (in m)?
2. 2.A square garden has an area of 2500 square m. How long is each side (in m)?
3. 3.Which of these is a perfect square? (a) 1396 (b) 1424 (c) 1369
4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 196 square m. How long is each side (in m)?
6. 6.A square garden has an area of 2809 square m. How long is each side (in m)?
7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
9. 9.How many whole numbers lie between 29² and 30²?
10. 10.A square garden has an area of 1936 square m. How long is each side (in m)?
11. 11.What is 97²? =
12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 144 square m. How long is each side (in m)?
14. 14.What is 49²? =
15. 15.What is 36²? =
16. 16.How many whole numbers lie between 21² and 22²?
17. 17.Which of these is a perfect square? (a) 1218 (b) 1156 (c) 1175
18. 18.What is 85²? =
19. 19.What is √1225? =
20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 275 must be divided to get a perfect square?
22. 22.A square garden has an area of 361 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 24² and 25²?
24. 24.A square garden has an area of 169 square m. How long is each side (in m)?
25. 25.What is √1600? =
26. 26.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
27. 27.Which of these is a perfect square? (a) 324 (b) 350 (c) 360
28. 28.What is √400? =
29. 29.Which of these is a perfect square? (a) 879 (b) 897 (c) 841
30. 30.What is 89²? =
31. 31.Which of these is a perfect square? (a) 196 (b) 202 (c) 217
32. 32.What is √4624? =
33. 33.What is the smallest whole number by which 490 must be divided to get a perfect square?
34. 34.How many whole numbers lie between 30² and 31²?
35. 35.What is 47²? =
36. 36.What is 72²? =
37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √3600? =
39. 39.What is √196? =
40. 40.Which of these is a perfect square? (a) 190 (b) 169 (c) 186

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