Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 626 · 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) 1225 (b) 1284 (c) 1273
2. 2.What is √121? =
3. 3.What is 14²? =
4. 4.What is the smallest whole number by which 160 must be divided to get a perfect square?
5. 5.Which of these is a perfect square? (a) 1563 (b) 1521 (c) 1592
6. 6.What is 46²? =
7. 7.What is √225? =
8. 8.What is 53²? =
9. 9.What is 88²? =
10. 10.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 13²? =
13. 13.How many whole numbers lie between 29² and 30²?
14. 14.What is √441? =
15. 15.A square garden has an area of 49 square m. How long is each side (in m)?
16. 16.What is √1369? =
17. 17.What is the smallest whole number by which 135 must be divided to get a perfect square?
18. 18.Which of these is a perfect square? (a) 893 (b) 862 (c) 841
19. 19.What is √841? =
20. 20.Which of these is a perfect square? (a) 496 (b) 484 (c) 494
21. 21.Which of these is a perfect square? (a) 428 (b) 410 (c) 400
22. 22.What is √9409? =
23. 23.Which of these is a perfect square? (a) 361 (b) 365 (c) 369
24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √169? =
28. 28.Which of these is a perfect square? (a) 625 (b) 634 (c) 667
29. 29.What is the smallest whole number by which 117 must be divided to get a perfect square?
30. 30.What is 26²? =
31. 31.Which of these is a perfect square? (a) 111 (b) 100 (c) 115
32. 32.Which of these is a perfect square? (a) 294 (b) 303 (c) 289
33. 33.How many whole numbers lie between 8² and 9²?
34. 34.What is 18²? =
35. 35.A square garden has an area of 121 square m. How long is each side (in m)?
36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
38. 38.A square garden has an area of 169 square m. How long is each side (in m)?
39. 39.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
40. 40.What is √1444? =

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