Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 300 · 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 175 must be divided to get a perfect square?
2. 2.What is √5625? =
3. 3.What is √576? =
4. 4.How many whole numbers lie between 32² and 33²?
5. 5.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
6. 6.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
7. 7.What is 12²? =
8. 8.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
9. 9.What is the smallest whole number by which 44 must be divided to get a perfect square?
10. 10.What is 52²? =
11. 11.Which of these is a perfect square? (a) 1089 (b) 1099 (c) 1139
12. 12.A square garden has an area of 441 square m. How long is each side (in m)?
13. 13.Which of these is a perfect square? (a) 256 (b) 266 (c) 263
14. 14.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
16. 16.What is 96²? =
17. 17.What is 82²? =
18. 18.What is √1024? =
19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 256 square m. How long is each side (in m)?
21. 21.What is √3481? =
22. 22.A square garden has an area of 36 square m. How long is each side (in m)?
23. 23.What is √2209? =
24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the smallest whole number by which 125 must be divided to get a perfect square?
26. 26.Which of these is a perfect square? (a) 729 (b) 733 (c) 781
27. 27.What is 97²? =
28. 28.Which of these is a perfect square? (a) 345 (b) 324 (c) 360
29. 29.How many whole numbers lie between 12² and 13²?
30. 30.A square garden has an area of 3025 square m. How long is each side (in m)?
31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 1189 (b) 1178 (c) 1156
33. 33.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
34. 34.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
35. 35.Which of these is a perfect square? (a) 116 (b) 102 (c) 100
36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √9025? =
38. 38.What is 85²? =
39. 39.What is 80²? =
40. 40.What is 22²? =

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