Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 699 · 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 18²? =
2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √361? =
4. 4.How many whole numbers lie between 19² and 20²?
5. 5.Which of these is a perfect square? (a) 584 (b) 576 (c) 580
6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 1369 (b) 1410 (c) 1439
8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 41²? =
10. 10.How many whole numbers lie between 28² and 29²?
11. 11.Which of these is a perfect square? (a) 441 (b) 468 (c) 476
12. 12.Which of these is a perfect square? (a) 1032 (b) 1024 (c) 1064
13. 13.What is √144? =
14. 14.What is √1600? =
15. 15.What is 12²? =
16. 16.What is 75²? =
17. 17.Which of these is a perfect square? (a) 282 (b) 256 (c) 287
18. 18.What is √5476? =
19. 19.Which of these is a perfect square? (a) 809 (b) 835 (c) 784
20. 20.What is 85²? =
21. 21.A square garden has an area of 2809 square m. How long is each side (in m)?
22. 22.A square garden has an area of 841 square m. How long is each side (in m)?
23. 23.What is 68²? =
24. 24.What is 40²? =
25. 25.What is the smallest whole number by which 320 must be divided to get a perfect square?
26. 26.What is 70²? =
27. 27.How many whole numbers lie between 27² and 28²?
28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
30. 30.How many whole numbers lie between 17² and 18²?
31. 31.What is 57²? =
32. 32.What is √2916? =
33. 33.Which of these is a perfect square? (a) 154 (b) 156 (c) 144
34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 69²? =
36. 36.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
37. 37.What is 71²? =
38. 38.Which of these is a perfect square? (a) 394 (b) 361 (c) 398
39. 39.Which of these is a perfect square? (a) 842 (b) 860 (c) 841
40. 40.Which of these is a perfect square? (a) 334 (b) 324 (c) 337

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