Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 410 · 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 √9025? =
2. 2.What is 33²? =
3. 3.A square garden has an area of 729 square m. How long is each side (in m)?
4. 4.What is 30²? =
5. 5.Which of these is a perfect square? (a) 1159 (b) 1197 (c) 1156
6. 6.How many whole numbers lie between 23² and 24²?
7. 7.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
8. 8.What is √1681? =
9. 9.What is the smallest whole number by which 192 must be divided to get a perfect square?
10. 10.What is √3844? =
11. 11.What is √8464? =
12. 12.What is 45²? =
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
14. 14.A square garden has an area of 100 square m. How long is each side (in m)?
15. 15.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √441? =
17. 17.What is √1764? =
18. 18.A square garden has an area of 1225 square m. How long is each side (in m)?
19. 19.What is 72²? =
20. 20.How many whole numbers lie between 42² and 43²?
21. 21.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
22. 22.What is 62²? =
23. 23.Which of these is a perfect square? (a) 118 (b) 119 (c) 100
24. 24.What is 70²? =
25. 25.What is √169? =
26. 26.Which of these is a perfect square? (a) 1521 (b) 1562 (c) 1574
27. 27.What is the smallest whole number by which 240 must be divided to get a perfect square?
28. 28.A square garden has an area of 784 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
31. 31.Which of these is a perfect square? (a) 1444 (b) 1509 (c) 1493
32. 32.What is 91²? =
33. 33.Which of these is a perfect square? (a) 400 (b) 431 (c) 423
34. 34.What is the smallest whole number by which 8 must be divided to get a perfect square?
35. 35.Which of these is a perfect square? (a) 169 (b) 185 (c) 192
36. 36.Which of these is a perfect square? (a) 304 (b) 295 (c) 289
37. 37.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
38. 38.What is √676? =
39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
40. 40.Which of these is a perfect square? (a) 256 (b) 271 (c) 267

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