Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 90 · 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 sum of the first 27 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 529 square m. How long is each side (in m)?
3. 3.What is the smallest whole number by which 448 must be divided to get a perfect square?
4. 4.What is 37²? =
5. 5.What is 36²? =
6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
7. 7.A square garden has an area of 441 square m. How long is each side (in m)?
8. 8.What is √3136? =
9. 9.How many whole numbers lie between 37² and 38²?
10. 10.What is √676? =
11. 11.What is the smallest whole number by which 960 must be divided to get a perfect square?
12. 12.A square garden has an area of 1849 square m. How long is each side (in m)?
13. 13.What is √5776? =
14. 14.How many whole numbers lie between 11² and 12²?
15. 15.How many whole numbers lie between 46² and 47²?
16. 16.What is √196? =
17. 17.A square garden has an area of 1600 square m. How long is each side (in m)?
18. 18.What is √484? =
19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √6084? =
21. 21.What is √1600? =
22. 22.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
23. 23.A square garden has an area of 324 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 822 (b) 838 (c) 784
25. 25.How many whole numbers lie between 13² and 14²?
26. 26.What is 16²? =
27. 27.How many whole numbers lie between 44² and 45²?
28. 28.What is √1156? =
29. 29.Which of these is a perfect square? (a) 1071 (b) 1086 (c) 1024
30. 30.What is the smallest whole number by which 1134 must be divided to get a perfect square?
31. 31.How many whole numbers lie between 29² and 30²?
32. 32.What is √2304? =
33. 33.What is 74²? =
34. 34.What is 22²? =
35. 35.What is 81²? =
36. 36.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √784? =
39. 39.What is 90²? =
40. 40.What is 73²? =

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