Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 163 · 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.Which of these is a perfect square? (a) 427 (b) 403 (c) 400
2. 2.What is √2916? =
3. 3.What is √1369? =
4. 4.What is the smallest whole number by which 832 must be divided to get a perfect square?
5. 5.How many whole numbers lie between 46² and 47²?
6. 6.How many whole numbers lie between 23² and 24²?
7. 7.What is √3600? =
8. 8.What is 64²? =
9. 9.A square garden has an area of 441 square m. How long is each side (in m)?
10. 10.What is √3249? =
11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
13. 13.What is 17²? =
14. 14.A square garden has an area of 400 square m. How long is each side (in m)?
15. 15.Which of these is a perfect square? (a) 900 (b) 934 (c) 930
16. 16.Which of these is a perfect square? (a) 840 (b) 784 (c) 822
17. 17.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
18. 18.What is 25²? =
19. 19.What is 24²? =
20. 20.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
21. 21.A square garden has an area of 2601 square m. How long is each side (in m)?
22. 22.A square garden has an area of 3249 square m. How long is each side (in m)?
23. 23.What is √169? =
24. 24.A square garden has an area of 121 square m. How long is each side (in m)?
25. 25.What is √9409? =
26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
27. 27.How many whole numbers lie between 17² and 18²?
28. 28.Which of these is a perfect square? (a) 175 (b) 187 (c) 169
29. 29.What is √784? =
30. 30.What is √7569? =
31. 31.Which of these is a perfect square? (a) 531 (b) 529 (c) 566
32. 32.What is 31²? =
33. 33.How many whole numbers lie between 21² and 22²?
34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √729? =
36. 36.Which of these is a perfect square? (a) 625 (b) 632 (c) 649
37. 37.Which of these is a perfect square? (a) 199 (b) 196 (c) 214
38. 38.A square garden has an area of 25 square m. How long is each side (in m)?
39. 39.A square garden has an area of 3025 square m. How long is each side (in m)?
40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?

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