Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 411 · 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.How many whole numbers lie between 42² and 43²?
2. 2.How many whole numbers lie between 31² and 32²?
3. 3.Which of these is a perfect square? (a) 576 (b) 584 (c) 585
4. 4.Which of these is a perfect square? (a) 926 (b) 910 (c) 900
5. 5.How many whole numbers lie between 43² and 44²?
6. 6.What is the smallest whole number by which 99 must be divided to get a perfect square?
7. 7.What is √5329? =
8. 8.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 21² and 22²?
10. 10.A square garden has an area of 256 square m. How long is each side (in m)?
11. 11.A square garden has an area of 324 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
13. 13.What is 28²? =
14. 14.What is √3249? =
15. 15.What is √1764? =
16. 16.Which of these is a perfect square? (a) 1225 (b) 1259 (c) 1266
17. 17.What is 43²? =
18. 18.How many whole numbers lie between 6² and 7²?
19. 19.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
20. 20.What is √961? =
21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 82²? =
23. 23.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
24. 24.What is 74²? =
25. 25.What is 66²? =
26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
28. 28.What is √144? =
29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
30. 30.What is 50²? =
31. 31.What is 31²? =
32. 32.How many whole numbers lie between 25² and 26²?
33. 33.A square garden has an area of 3600 square m. How long is each side (in m)?
34. 34.Which of these is a perfect square? (a) 384 (b) 396 (c) 361
35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
36. 36.What is √1681? =
37. 37.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 37² and 38²?
39. 39.What is the smallest whole number by which 360 must be divided to get a perfect square?
40. 40.What is the smallest whole number by which 54 must be multiplied to get a perfect square?

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