Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 734 · 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 31²? =
2. 2.A square garden has an area of 1521 square m. How long is each side (in m)?
3. 3.A square garden has an area of 100 square m. How long is each side (in m)?
4. 4.What is √841? =
5. 5.How many whole numbers lie between 10² and 11²?
6. 6.A square garden has an area of 324 square m. How long is each side (in m)?
7. 7.What is √9216? =
8. 8.How many whole numbers lie between 26² and 27²?
9. 9.How many whole numbers lie between 35² and 36²?
10. 10.Which of these is a perfect square? (a) 1574 (b) 1521 (c) 1533
11. 11.What is 59²? =
12. 12.What is √4624? =
13. 13.What is the smallest whole number by which 180 must be divided to get a perfect square?
14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
15. 15.Which of these is a perfect square? (a) 144 (b) 168 (c) 165
16. 16.What is √225? =
17. 17.What is the smallest whole number by which 160 must be divided to get a perfect square?
18. 18.What is √121? =
19. 19.What is √2916? =
20. 20.How many whole numbers lie between 19² and 20²?
21. 21.Which of these is a perfect square? (a) 1600 (b) 1603 (c) 1669
22. 22.What is √8836? =
23. 23.What is 61²? =
24. 24.What is 41²? =
25. 25.What is 18²? =
26. 26.A square garden has an area of 441 square m. How long is each side (in m)?
27. 27.What is 88²? =
28. 28.Which of these is a perfect square? (a) 620 (b) 608 (c) 576
29. 29.What is √2116? =
30. 30.How many whole numbers lie between 30² and 31²?
31. 31.Which of these is a perfect square? (a) 223 (b) 204 (c) 196
32. 32.A square garden has an area of 169 square m. How long is each side (in m)?
33. 33.How many whole numbers lie between 49² and 50²?
34. 34.A square garden has an area of 2916 square m. How long is each side (in m)?
35. 35.What is 39²? =
36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 28²? =
38. 38.A square garden has an area of 3364 square m. How long is each side (in m)?
39. 39.A square garden has an area of 3025 square m. How long is each side (in m)?
40. 40.What is √2809? =

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