Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 529 · 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 √2809? =
2. 2.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 81²? =
5. 5.What is √3136? =
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.How many whole numbers lie between 9² and 10²?
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
9. 9.Which of these is a perfect square? (a) 543 (b) 539 (c) 529
10. 10.A square garden has an area of 2116 square m. How long is each side (in m)?
11. 11.How many whole numbers lie between 14² and 15²?
12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 130 (b) 143 (c) 121
14. 14.What is √3721? =
15. 15.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
16. 16.How many whole numbers lie between 46² and 47²?
17. 17.What is √4761? =
18. 18.A square garden has an area of 841 square m. How long is each side (in m)?
19. 19.A square garden has an area of 2025 square m. How long is each side (in m)?
20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 20 must be divided to get a perfect square?
22. 22.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
23. 23.What is the smallest whole number by which 540 must be divided to get a perfect square?
24. 24.What is √324? =
25. 25.What is √4489? =
26. 26.How many whole numbers lie between 29² and 30²?
27. 27.What is the smallest whole number by which 325 must be divided to get a perfect square?
28. 28.What is √3249? =
29. 29.What is 16²? =
30. 30.What is 30²? =
31. 31.Which of these is a perfect square? (a) 106 (b) 103 (c) 100
32. 32.What is √169? =
33. 33.What is 54²? =
34. 34.A square garden has an area of 49 square m. How long is each side (in m)?
35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
36. 36.How many whole numbers lie between 42² and 43²?
37. 37.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
38. 38.Which of these is a perfect square? (a) 326 (b) 324 (c) 355
39. 39.What is √1681? =
40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

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