Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 225 · 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 28² and 29²?
2. 2.A square garden has an area of 36 square m. How long is each side (in m)?
3. 3.A square garden has an area of 169 square m. How long is each side (in m)?
4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
5. 5.Which of these is a perfect square? (a) 1305 (b) 1328 (c) 1296
6. 6.Which of these is a perfect square? (a) 324 (b) 347 (c) 330
7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
9. 9.What is 75²? =
10. 10.What is 35²? =
11. 11.What is 30²? =
12. 12.How many whole numbers lie between 32² and 33²?
13. 13.What is √4900? =
14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
15. 15.A square garden has an area of 100 square m. How long is each side (in m)?
16. 16.What is 54²? =
17. 17.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
20. 20.How many whole numbers lie between 48² and 49²?
21. 21.What is the smallest whole number by which 175 must be divided to get a perfect square?
22. 22.What is 46²? =
23. 23.How many whole numbers lie between 6² and 7²?
24. 24.What is √169? =
25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
27. 27.What is 91²? =
28. 28.What is √225? =
29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √8649? =
31. 31.What is √9604? =
32. 32.A square garden has an area of 1521 square m. How long is each side (in m)?
33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 3600 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 100 (b) 103 (c) 111
36. 36.A square garden has an area of 256 square m. How long is each side (in m)?
37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 36² and 37²?
39. 39.What is 31²? =
40. 40.Which of these is a perfect square? (a) 314 (b) 307 (c) 289

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