Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 25 · 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 180 must be multiplied to get a perfect square?
2. 2.Which of these is a perfect square? (a) 1296 (b) 1366 (c) 1352
3. 3.A square garden has an area of 169 square m. How long is each side (in m)?
4. 4.What is the smallest whole number by which 960 must be divided to get a perfect square?
5. 5.What is 98²? =
6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √8649? =
8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 1936 square m. How long is each side (in m)?
11. 11.What is √2209? =
12. 12.What is √676? =
13. 13.Which of these is a perfect square? (a) 111 (b) 100 (c) 106
14. 14.What is 91²? =
15. 15.Which of these is a perfect square? (a) 1496 (b) 1520 (c) 1444
16. 16.A square garden has an area of 196 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 456 (b) 441 (c) 472
18. 18.What is the smallest whole number by which 325 must be divided to get a perfect square?
19. 19.What is 90²? =
20. 20.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 926 (b) 941 (c) 900
22. 22.Which of these is a perfect square? (a) 1521 (b) 1530 (c) 1593
23. 23.A square garden has an area of 1024 square m. How long is each side (in m)?
24. 24.A square garden has an area of 2916 square m. How long is each side (in m)?
25. 25.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
26. 26.What is 53²? =
27. 27.What is √3481? =
28. 28.What is the smallest whole number by which 108 must be divided to get a perfect square?
29. 29.What is 12²? =
30. 30.What is √4096? =
31. 31.A square garden has an area of 729 square m. How long is each side (in m)?
32. 32.How many whole numbers lie between 40² and 41²?
33. 33.What is the smallest whole number by which 175 must be divided to get a perfect square?
34. 34.A square garden has an area of 1521 square m. How long is each side (in m)?
35. 35.A square garden has an area of 784 square m. How long is each side (in m)?
36. 36.What is 89²? =
37. 37.What is 17²? =
38. 38.What is 79²? =
39. 39.What is √5041? =
40. 40.What is √1369? =

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