Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 158 · 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 multiplied to get a perfect square?
2. 2.What is 80²? =
3. 3.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
4. 4.Which of these is a perfect square? (a) 1156 (b) 1178 (c) 1194
5. 5.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
6. 6.What is √3249? =
7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √2916? =
9. 9.What is 79²? =
10. 10.How many whole numbers lie between 34² and 35²?
11. 11.What is 21²? =
12. 12.A square garden has an area of 441 square m. How long is each side (in m)?
13. 13.What is 33²? =
14. 14.What is the smallest whole number by which 686 must be divided to get a perfect square?
15. 15.How many whole numbers lie between 25² and 26²?
16. 16.What is √1089? =
17. 17.What is 91²? =
18. 18.A square garden has an area of 49 square m. How long is each side (in m)?
19. 19.What is √3481? =
20. 20.A square garden has an area of 121 square m. How long is each side (in m)?
21. 21.What is 82²? =
22. 22.What is the smallest whole number by which 960 must be divided to get a perfect square?
23. 23.What is the smallest whole number by which 350 must be divided to get a perfect square?
24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 10² and 11²?
26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
27. 27.What is 43²? =
28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
29. 29.What is 78²? =
30. 30.What is 98²? =
31. 31.What is the smallest whole number by which 637 must be divided to get a perfect square?
32. 32.What is √225? =
33. 33.What is 23²? =
34. 34.What is 57²? =
35. 35.What is 47²? =
36. 36.What is √5625? =
37. 37.A square garden has an area of 361 square m. How long is each side (in m)?
38. 38.What is 72²? =
39. 39.What is the smallest whole number by which 117 must be divided to get a perfect square?
40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?

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