Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 208 · 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 smallest whole number by which 24 must be divided to get a perfect square?
2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
5. 5.What is √196? =
6. 6.How many whole numbers lie between 5² and 6²?
7. 7.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
8. 8.Which of these is a perfect square? (a) 484 (b) 515 (c) 493
9. 9.A square garden has an area of 2809 square m. How long is each side (in m)?
10. 10.Which of these is a perfect square? (a) 1296 (b) 1331 (c) 1315
11. 11.What is 33²? =
12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
13. 13.What is 62²? =
14. 14.Which of these is a perfect square? (a) 1039 (b) 1024 (c) 1045
15. 15.What is the smallest whole number by which 125 must be divided to get a perfect square?
16. 16.A square garden has an area of 3025 square m. How long is each side (in m)?
17. 17.What is √256? =
18. 18.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
19. 19.What is √4356? =
20. 20.Which of these is a perfect square? (a) 310 (b) 289 (c) 303
21. 21.A square garden has an area of 2209 square m. How long is each side (in m)?
22. 22.What is √2401? =
23. 23.What is √3481? =
24. 24.What is 40²? =
25. 25.A square garden has an area of 2500 square m. How long is each side (in m)?
26. 26.How many whole numbers lie between 30² and 31²?
27. 27.What is 49²? =
28. 28.What is 66²? =
29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
30. 30.What is 56²? =
31. 31.How many whole numbers lie between 33² and 34²?
32. 32.How many whole numbers lie between 21² and 22²?
33. 33.What is √3249? =
34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 17²? =
36. 36.A square garden has an area of 576 square m. How long is each side (in m)?
37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 61²? =
40. 40.What is 50²? =

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