Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 404 · 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) 292 (b) 289 (c) 309
2. 2.What is √1156? =
3. 3.Which of these is a perfect square? (a) 102 (b) 100 (c) 106
4. 4.A square garden has an area of 100 square m. How long is each side (in m)?
5. 5.What is 85²? =
6. 6.What is 36²? =
7. 7.What is √441? =
8. 8.What is 71²? =
9. 9.A square garden has an area of 49 square m. How long is each side (in m)?
10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 12 must be divided to get a perfect square?
12. 12.What is 12²? =
13. 13.How many whole numbers lie between 34² and 35²?
14. 14.How many whole numbers lie between 40² and 41²?
15. 15.A square garden has an area of 784 square m. How long is each side (in m)?
16. 16.A square garden has an area of 196 square m. How long is each side (in m)?
17. 17.What is 91²? =
18. 18.Which of these is a perfect square? (a) 494 (b) 503 (c) 484
19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 540 (b) 550 (c) 529
21. 21.How many whole numbers lie between 33² and 34²?
22. 22.Which of these is a perfect square? (a) 1133 (b) 1089 (c) 1091
23. 23.What is 99²? =
24. 24.Which of these is a perfect square? (a) 1505 (b) 1509 (c) 1444
25. 25.How many whole numbers lie between 24² and 25²?
26. 26.What is √3844? =
27. 27.What is the smallest whole number by which 176 must be divided to get a perfect square?
28. 28.What is 55²? =
29. 29.A square garden has an area of 1444 square m. How long is each side (in m)?
30. 30.What is the smallest whole number by which 540 must be divided to get a perfect square?
31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
33. 33.How many whole numbers lie between 22² and 23²?
34. 34.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 75²? =
37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
38. 38.Which of these is a perfect square? (a) 910 (b) 900 (c) 917
39. 39.What is 72²? =
40. 40.What is the smallest whole number by which 325 must be divided to get a perfect square?

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