Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 514 · 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 18 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 540 must be divided to get a perfect square?
3. 3.What is √1296? =
4. 4.How many whole numbers lie between 5² and 6²?
5. 5.What is √625? =
6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
9. 9.How many whole numbers lie between 44² and 45²?
10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 15²? =
12. 12.What is √8649? =
13. 13.What is 74²? =
14. 14.What is 17²? =
15. 15.What is 79²? =
16. 16.What is the smallest whole number by which 1134 must be divided to get a perfect square?
17. 17.What is 60²? =
18. 18.A square garden has an area of 225 square m. How long is each side (in m)?
19. 19.What is 64²? =
20. 20.What is 34²? =
21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
23. 23.What is √6084? =
24. 24.How many whole numbers lie between 30² and 31²?
25. 25.What is 25²? =
26. 26.A square garden has an area of 196 square m. How long is each side (in m)?
27. 27.How many whole numbers lie between 35² and 36²?
28. 28.What is √484? =
29. 29.Which of these is a perfect square? (a) 841 (b) 860 (c) 869
30. 30.How many whole numbers lie between 31² and 32²?
31. 31.What is √3969? =
32. 32.What is √6241? =
33. 33.What is √4225? =
34. 34.What is √256? =
35. 35.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
37. 37.A square garden has an area of 2209 square m. How long is each side (in m)?
38. 38.What is 21²? =
39. 39.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

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