Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 275 · 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 √2916? =
2. 2.What is 61²? =
3. 3.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 53²? =
5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
6. 6.What is √8836? =
7. 7.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
8. 8.What is 85²? =
9. 9.Which of these is a perfect square? (a) 1156 (b) 1180 (c) 1213
10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 73²? =
12. 12.A square garden has an area of 3249 square m. How long is each side (in m)?
13. 13.How many whole numbers lie between 5² and 6²?
14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
15. 15.How many whole numbers lie between 7² and 8²?
16. 16.A square garden has an area of 1681 square m. How long is each side (in m)?
17. 17.What is √5929? =
18. 18.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √7056? =
21. 21.What is √1024? =
22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the smallest whole number by which 75 must be divided to get a perfect square?
24. 24.What is 96²? =
25. 25.What is √1936? =
26. 26.A square garden has an area of 64 square m. How long is each side (in m)?
27. 27.Which of these is a perfect square? (a) 1600 (b) 1616 (c) 1607
28. 28.How many whole numbers lie between 27² and 28²?
29. 29.A square garden has an area of 441 square m. How long is each side (in m)?
30. 30.A square garden has an area of 49 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
32. 32.What is 92²? =
33. 33.A square garden has an area of 841 square m. How long is each side (in m)?
34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
35. 35.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
36. 36.What is the smallest whole number by which 490 must be divided to get a perfect square?
37. 37.A square garden has an area of 3025 square m. How long is each side (in m)?
38. 38.A square garden has an area of 324 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 1349 (b) 1367 (c) 1296
40. 40.What is 76²? =

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