Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 509 · 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 smallest whole number by which 18 must be divided to get a perfect square?
2. 2.A square garden has an area of 100 square m. How long is each side (in m)?
3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
4. 4.A square garden has an area of 3249 square m. How long is each side (in m)?
5. 5.What is 87²? =
6. 6.How many whole numbers lie between 46² and 47²?
7. 7.What is √484? =
8. 8.How many whole numbers lie between 48² and 49²?
9. 9.How many whole numbers lie between 31² and 32²?
10. 10.Which of these is a perfect square? (a) 1160 (b) 1205 (c) 1156
11. 11.What is √3844? =
12. 12.Which of these is a perfect square? (a) 1444 (b) 1488 (c) 1453
13. 13.What is 96²? =
14. 14.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 14² and 15²?
17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √6561? =
20. 20.What is the smallest whole number by which 8 must be divided to get a perfect square?
21. 21.How many whole numbers lie between 37² and 38²?
22. 22.What is √2401? =
23. 23.A square garden has an area of 441 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 511 (b) 500 (c) 484
25. 25.What is 13²? =
26. 26.Which of these is a perfect square? (a) 263 (b) 270 (c) 256
27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √2601? =
29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
30. 30.A square garden has an area of 529 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
32. 32.A square garden has an area of 2916 square m. How long is each side (in m)?
33. 33.A square garden has an area of 81 square m. How long is each side (in m)?
34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 23²? =
36. 36.How many whole numbers lie between 22² and 23²?
37. 37.What is √7744? =
38. 38.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 21²? =
40. 40.Which of these is a perfect square? (a) 1602 (b) 1630 (c) 1600

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