Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 715 · 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 93²? =
2. 2.What is √9801? =
3. 3.What is the smallest whole number by which 896 must be divided to get a perfect square?
4. 4.A square garden has an area of 64 square m. How long is each side (in m)?
5. 5.What is √7921? =
6. 6.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
7. 7.Which of these is a perfect square? (a) 1417 (b) 1434 (c) 1369
8. 8.What is 83²? =
9. 9.How many whole numbers lie between 34² and 35²?
10. 10.What is √196? =
11. 11.A square garden has an area of 225 square m. How long is each side (in m)?
12. 12.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 121 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 22² and 23²?
15. 15.A square garden has an area of 1936 square m. How long is each side (in m)?
16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √289? =
19. 19.How many whole numbers lie between 31² and 32²?
20. 20.How many whole numbers lie between 27² and 28²?
21. 21.How many whole numbers lie between 33² and 34²?
22. 22.Which of these is a perfect square? (a) 645 (b) 625 (c) 635
23. 23.How many whole numbers lie between 12² and 13²?
24. 24.Which of these is a perfect square? (a) 585 (b) 587 (c) 576
25. 25.A square garden has an area of 625 square m. How long is each side (in m)?
26. 26.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
27. 27.What is √2500? =
28. 28.How many whole numbers lie between 25² and 26²?
29. 29.What is √529? =
30. 30.Which of these is a perfect square? (a) 557 (b) 564 (c) 529
31. 31.What is √7569? =
32. 32.Which of these is a perfect square? (a) 162 (b) 166 (c) 144
33. 33.What is 96²? =
34. 34.Which of these is a perfect square? (a) 459 (b) 441 (c) 479
35. 35.What is √5329? =
36. 36.Which of these is a perfect square? (a) 1329 (b) 1325 (c) 1296
37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 753 (b) 729 (c) 763
40. 40.What is √1936? =

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