Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 258 · 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.How many whole numbers lie between 15² and 16²?
2. 2.Which of these is a perfect square? (a) 1513 (b) 1444 (c) 1467
3. 3.Which of these is a perfect square? (a) 196 (b) 215 (c) 209
4. 4.A square garden has an area of 3481 square m. How long is each side (in m)?
5. 5.What is 44²? =
6. 6.What is 29²? =
7. 7.What is 67²? =
8. 8.What is √441? =
9. 9.A square garden has an area of 729 square m. How long is each side (in m)?
10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 907 (b) 915 (c) 900
12. 12.What is √3721? =
13. 13.What is 18²? =
14. 14.How many whole numbers lie between 27² and 28²?
15. 15.Which of these is a perfect square? (a) 1174 (b) 1156 (c) 1203
16. 16.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
17. 17.What is √361? =
18. 18.A square garden has an area of 361 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
20. 20.How many whole numbers lie between 18² and 19²?
21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 25²? =
23. 23.What is √8100? =
24. 24.What is 94²? =
25. 25.What is √7921? =
26. 26.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
27. 27.What is 80²? =
28. 28.Which of these is a perfect square? (a) 441 (b) 466 (c) 471
29. 29.A square garden has an area of 2304 square m. How long is each side (in m)?
30. 30.What is 47²? =
31. 31.What is 68²? =
32. 32.Which of these is a perfect square? (a) 327 (b) 356 (c) 324
33. 33.A square garden has an area of 3600 square m. How long is each side (in m)?
34. 34.What is 38²? =
35. 35.What is 72²? =
36. 36.Which of these is a perfect square? (a) 121 (b) 141 (c) 130
37. 37.How many whole numbers lie between 12² and 13²?
38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
39. 39.A square garden has an area of 961 square m. How long is each side (in m)?
40. 40.What is √1369? =

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