Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 426 · 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 96²? =
2. 2.What is √8464? =
3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 1555 (b) 1521 (c) 1551
5. 5.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
6. 6.What is 38²? =
7. 7.Which of these is a perfect square? (a) 1225 (b) 1237 (c) 1269
8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
10. 10.What is 20²? =
11. 11.What is 66²? =
12. 12.What is 12²? =
13. 13.What is √900? =
14. 14.What is 61²? =
15. 15.How many whole numbers lie between 44² and 45²?
16. 16.Which of these is a perfect square? (a) 1444 (b) 1500 (c) 1506
17. 17.What is the smallest whole number by which 275 must be divided to get a perfect square?
18. 18.How many whole numbers lie between 42² and 43²?
19. 19.A square garden has an area of 2601 square m. How long is each side (in m)?
20. 20.How many whole numbers lie between 20² and 21²?
21. 21.What is 32²? =
22. 22.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
23. 23.A square garden has an area of 2209 square m. How long is each side (in m)?
24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
25. 25.Which of these is a perfect square? (a) 363 (b) 388 (c) 361
26. 26.What is 29²? =
27. 27.A square garden has an area of 49 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 18² and 19²?
29. 29.Which of these is a perfect square? (a) 174 (b) 176 (c) 169
30. 30.How many whole numbers lie between 5² and 6²?
31. 31.What is 89²? =
32. 32.How many whole numbers lie between 6² and 7²?
33. 33.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
34. 34.What is 26²? =
35. 35.What is √484? =
36. 36.What is √225? =
37. 37.What is 33²? =
38. 38.What is 85²? =
39. 39.What is 37²? =
40. 40.What is the smallest whole number by which 75 must be divided to get a perfect square?

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