Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 614 · 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) 1168 (b) 1156 (c) 1183
2. 2.Which of these is a perfect square? (a) 1513 (b) 1444 (c) 1518
3. 3.A square garden has an area of 289 square m. How long is each side (in m)?
4. 4.What is 62²? =
5. 5.How many whole numbers lie between 37² and 38²?
6. 6.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 312 (b) 289 (c) 291
8. 8.What is the smallest whole number by which 125 must be divided to get a perfect square?
9. 9.What is √9025? =
10. 10.What is √1444? =
11. 11.A square garden has an area of 3600 square m. How long is each side (in m)?
12. 12.What is √8836? =
13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √5476? =
15. 15.What is the smallest whole number by which 208 must be divided to get a perfect square?
16. 16.A square garden has an area of 100 square m. How long is each side (in m)?
17. 17.What is √841? =
18. 18.Which of these is a perfect square? (a) 249 (b) 240 (c) 225
19. 19.What is √576? =
20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
21. 21.What is 97²? =
22. 22.Which of these is a perfect square? (a) 109 (b) 100 (c) 105
23. 23.A square garden has an area of 1936 square m. How long is each side (in m)?
24. 24.What is 42²? =
25. 25.What is 22²? =
26. 26.Which of these is a perfect square? (a) 592 (b) 576 (c) 600
27. 27.What is the smallest whole number by which 147 must be divided to get a perfect square?
28. 28.A square garden has an area of 961 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 35² and 36²?
30. 30.What is √169? =
31. 31.What is 39²? =
32. 32.What is 47²? =
33. 33.How many whole numbers lie between 17² and 18²?
34. 34.Which of these is a perfect square? (a) 648 (b) 654 (c) 625
35. 35.A square garden has an area of 1369 square m. How long is each side (in m)?
36. 36.Which of these is a perfect square? (a) 729 (b) 777 (c) 768
37. 37.What is √1936? =
38. 38.What is 90²? =
39. 39.Which of these is a perfect square? (a) 187 (b) 169 (c) 184
40. 40.What is 73²? =

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