Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 10 · 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 11 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 22² and 23²?
3. 3.How many whole numbers lie between 49² and 50²?
4. 4.How many whole numbers lie between 47² and 48²?
5. 5.What is √400? =
6. 6.A square garden has an area of 529 square m. How long is each side (in m)?
7. 7.How many whole numbers lie between 26² and 27²?
8. 8.A square garden has an area of 3364 square m. How long is each side (in m)?
9. 9.A square garden has an area of 25 square m. How long is each side (in m)?
10. 10.A square garden has an area of 196 square m. How long is each side (in m)?
11. 11.How many whole numbers lie between 34² and 35²?
12. 12.What is √3721? =
13. 13.What is 80²? =
14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 31²? =
16. 16.What is 91²? =
17. 17.A square garden has an area of 2025 square m. How long is each side (in m)?
18. 18.Which of these is a perfect square? (a) 144 (b) 168 (c) 153
19. 19.A square garden has an area of 1600 square m. How long is each side (in m)?
20. 20.Which of these is a perfect square? (a) 225 (b) 250 (c) 241
21. 21.How many whole numbers lie between 18² and 19²?
22. 22.Which of these is a perfect square? (a) 441 (b) 448 (c) 479
23. 23.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
24. 24.What is 96²? =
25. 25.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
26. 26.What is 93²? =
27. 27.A square garden has an area of 100 square m. How long is each side (in m)?
28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 8² and 9²?
30. 30.How many whole numbers lie between 24² and 25²?
31. 31.What is 75²? =
32. 32.How many whole numbers lie between 14² and 15²?
33. 33.What is √1024? =
34. 34.What is the smallest whole number by which 175 must be divided to get a perfect square?
35. 35.What is 22²? =
36. 36.How many whole numbers lie between 11² and 12²?
37. 37.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
38. 38.What is 99²? =
39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
40. 40.What is √225? =

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