Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 543 · 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 √1521? =
2. 2.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
3. 3.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
4. 4.What is 94²? =
5. 5.Which of these is a perfect square? (a) 147 (b) 144 (c) 164
6. 6.How many whole numbers lie between 5² and 6²?
7. 7.What is √784? =
8. 8.A square garden has an area of 484 square m. How long is each side (in m)?
9. 9.What is √8836? =
10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 36 square m. How long is each side (in m)?
12. 12.What is √4225? =
13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 11²? =
15. 15.What is the smallest whole number by which 192 must be divided to get a perfect square?
16. 16.What is 30²? =
17. 17.What is the smallest whole number by which 637 must be divided to get a perfect square?
18. 18.What is √7056? =
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 961 square m. How long is each side (in m)?
21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
22. 22.A square garden has an area of 2401 square m. How long is each side (in m)?
23. 23.What is 90²? =
24. 24.What is 82²? =
25. 25.What is √324? =
26. 26.Which of these is a perfect square? (a) 219 (b) 222 (c) 196
27. 27.Which of these is a perfect square? (a) 531 (b) 561 (c) 529
28. 28.A square garden has an area of 1156 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 11² and 12²?
30. 30.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
31. 31.What is 68²? =
32. 32.What is 99²? =
33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
35. 35.What is 70²? =
36. 36.How many whole numbers lie between 39² and 40²?
37. 37.A square garden has an area of 100 square m. How long is each side (in m)?
38. 38.What is the smallest whole number by which 80 must be divided to get a perfect square?
39. 39.Which of these is a perfect square? (a) 982 (b) 961 (c) 978
40. 40.What is the smallest whole number by which 567 must be divided to get a perfect square?

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