Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 594 · 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.A square garden has an area of 1089 square m. How long is each side (in m)?
2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the smallest whole number by which 396 must be divided to get a perfect square?
4. 4.Which of these is a perfect square? (a) 196 (b) 201 (c) 220
5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √1225? =
7. 7.A square garden has an area of 121 square m. How long is each side (in m)?
8. 8.What is 90²? =
9. 9.What is √9216? =
10. 10.What is 79²? =
11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
12. 12.How many whole numbers lie between 29² and 30²?
13. 13.A square garden has an area of 225 square m. How long is each side (in m)?
14. 14.What is √576? =
15. 15.What is √196? =
16. 16.Which of these is a perfect square? (a) 168 (b) 144 (c) 164
17. 17.How many whole numbers lie between 17² and 18²?
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 44²? =
20. 20.What is 69²? =
21. 21.What is 76²? =
22. 22.Which of these is a perfect square? (a) 1427 (b) 1383 (c) 1369
23. 23.What is 53²? =
24. 24.What is 49²? =
25. 25.What is 16²? =
26. 26.How many whole numbers lie between 28² and 29²?
27. 27.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
28. 28.What is √900? =
29. 29.How many whole numbers lie between 18² and 19²?
30. 30.How many whole numbers lie between 14² and 15²?
31. 31.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
32. 32.Which of these is a perfect square? (a) 1368 (b) 1330 (c) 1296
33. 33.What is √2704? =
34. 34.How many whole numbers lie between 48² and 49²?
35. 35.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
36. 36.How many whole numbers lie between 43² and 44²?
37. 37.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
38. 38.A square garden has an area of 2916 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 23² and 24²?
40. 40.What is 94²? =

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