Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 450 · 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 20 must be multiplied to get a perfect square?
2. 2.What is √1600? =
3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 216 (b) 196 (c) 215
5. 5.What is √4624? =
6. 6.What is 49²? =
7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √576? =
9. 9.A square garden has an area of 100 square m. How long is each side (in m)?
10. 10.What is √5041? =
11. 11.What is √900? =
12. 12.What is 37²? =
13. 13.What is √9025? =
14. 14.A square garden has an area of 225 square m. How long is each side (in m)?
15. 15.How many whole numbers lie between 5² and 6²?
16. 16.What is the smallest whole number by which 99 must be divided to get a perfect square?
17. 17.How many whole numbers lie between 33² and 34²?
18. 18.What is √4225? =
19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 1434 (b) 1370 (c) 1369
21. 21.What is 98²? =
22. 22.What is √4356? =
23. 23.What is the smallest whole number by which 224 must be divided to get a perfect square?
24. 24.What is the smallest whole number by which 147 must be divided to get a perfect square?
25. 25.What is √8649? =
26. 26.How many whole numbers lie between 14² and 15²?
27. 27.A square garden has an area of 81 square m. How long is each side (in m)?
28. 28.What is √2116? =
29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
30. 30.How many whole numbers lie between 47² and 48²?
31. 31.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
32. 32.What is 18²? =
33. 33.What is √4489? =
34. 34.A square garden has an area of 196 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 29² and 30²?
36. 36.A square garden has an area of 324 square m. How long is each side (in m)?
37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 563 (b) 532 (c) 529
40. 40.What is 40²? =

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