Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 198 · 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) 169 (b) 176 (c) 195
2. 2.Which of these is a perfect square? (a) 441 (b) 452 (c) 465
3. 3.A square garden has an area of 529 square m. How long is each side (in m)?
4. 4.What is √1369? =
5. 5.What is 19²? =
6. 6.What is 61²? =
7. 7.Which of these is a perfect square? (a) 233 (b) 225 (c) 238
8. 8.What is 34²? =
9. 9.A square garden has an area of 2025 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 289 (b) 312 (c) 295
13. 13.Which of these is a perfect square? (a) 784 (b) 790 (c) 798
14. 14.What is √225? =
15. 15.A square garden has an area of 49 square m. How long is each side (in m)?
16. 16.What is 60²? =
17. 17.How many whole numbers lie between 27² and 28²?
18. 18.Which of these is a perfect square? (a) 743 (b) 729 (c) 766
19. 19.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
20. 20.What is the smallest whole number by which 99 must be divided to get a perfect square?
21. 21.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
22. 22.A square garden has an area of 3600 square m. How long is each side (in m)?
23. 23.What is the smallest whole number by which 27 must be divided to get a perfect square?
24. 24.What is √2601? =
25. 25.What is √6241? =
26. 26.What is 74²? =
27. 27.A square garden has an area of 121 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 47² and 48²?
29. 29.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √9409? =
32. 32.How many whole numbers lie between 17² and 18²?
33. 33.What is 94²? =
34. 34.How many whole numbers lie between 9² and 10²?
35. 35.A square garden has an area of 289 square m. How long is each side (in m)?
36. 36.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
37. 37.A square garden has an area of 1764 square m. How long is each side (in m)?
38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √4900? =
40. 40.What is 38²? =

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