Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 62 · 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 √7921? =
2. 2.A square garden has an area of 2401 square m. How long is each side (in m)?
3. 3.What is 80²? =
4. 4.A square garden has an area of 196 square m. How long is each side (in m)?
5. 5.What is √2809? =
6. 6.What is the smallest whole number by which 44 must be divided to get a perfect square?
7. 7.How many whole numbers lie between 13² and 14²?
8. 8.What is 37²? =
9. 9.Which of these is a perfect square? (a) 829 (b) 835 (c) 784
10. 10.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
11. 11.A square garden has an area of 2916 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
13. 13.What is 93²? =
14. 14.What is 61²? =
15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
16. 16.What is 39²? =
17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the smallest whole number by which 63 must be divided to get a perfect square?
20. 20.A square garden has an area of 1089 square m. How long is each side (in m)?
21. 21.What is 54²? =
22. 22.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
23. 23.What is 21²? =
24. 24.What is 44²? =
25. 25.What is √484? =
26. 26.What is 89²? =
27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the smallest whole number by which 810 must be divided to get a perfect square?
30. 30.Which of these is a perfect square? (a) 934 (b) 906 (c) 900
31. 31.What is 78²? =
32. 32.A square garden has an area of 144 square m. How long is each side (in m)?
33. 33.What is √8464? =
34. 34.How many whole numbers lie between 27² and 28²?
35. 35.What is √841? =
36. 36.Which of these is a perfect square? (a) 671 (b) 625 (c) 632
37. 37.What is the smallest whole number by which 8 must be divided to get a perfect square?
38. 38.What is the smallest whole number by which 243 must be divided to get a perfect square?
39. 39.How many whole numbers lie between 35² and 36²?
40. 40.What is 25²? =

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