Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 680 · 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.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
2. 2.What is √3136? =
3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 1631 (b) 1643 (c) 1600
5. 5.What is 50²? =
6. 6.What is √3025? =
7. 7.A square garden has an area of 1936 square m. How long is each side (in m)?
8. 8.How many whole numbers lie between 18² and 19²?
9. 9.Which of these is a perfect square? (a) 1003 (b) 1016 (c) 961
10. 10.Which of these is a perfect square? (a) 100 (b) 106 (c) 117
11. 11.What is 22²? =
12. 12.A square garden has an area of 841 square m. How long is each side (in m)?
13. 13.What is 75²? =
14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √5776? =
16. 16.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
17. 17.How many whole numbers lie between 43² and 44²?
18. 18.What is √1024? =
19. 19.Which of these is a perfect square? (a) 292 (b) 289 (c) 312
20. 20.A square garden has an area of 1849 square m. How long is each side (in m)?
21. 21.What is √3721? =
22. 22.Which of these is a perfect square? (a) 359 (b) 324 (c) 356
23. 23.A square garden has an area of 1444 square m. How long is each side (in m)?
24. 24.What is the smallest whole number by which 18 must be divided to get a perfect square?
25. 25.What is 37²? =
26. 26.Which of these is a perfect square? (a) 121 (b) 122 (c) 137
27. 27.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 511 (b) 497 (c) 484
30. 30.What is 70²? =
31. 31.How many whole numbers lie between 48² and 49²?
32. 32.How many whole numbers lie between 44² and 45²?
33. 33.What is √9604? =
34. 34.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
35. 35.A square garden has an area of 2116 square m. How long is each side (in m)?
36. 36.What is √225? =
37. 37.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 23² and 24²?
39. 39.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
40. 40.What is √4489? =

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