Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 370 · 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 √7225? =
2. 2.A square garden has an area of 2304 square m. How long is each side (in m)?
3. 3.What is √169? =
4. 4.What is √441? =
5. 5.A square garden has an area of 100 square m. How long is each side (in m)?
6. 6.What is √5929? =
7. 7.What is 67²? =
8. 8.Which of these is a perfect square? (a) 900 (b) 956 (c) 905
9. 9.What is 34²? =
10. 10.Which of these is a perfect square? (a) 1058 (b) 1024 (c) 1037
11. 11.What is 73²? =
12. 12.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
13. 13.What is 80²? =
14. 14.What is 45²? =
15. 15.What is √4900? =
16. 16.How many whole numbers lie between 27² and 28²?
17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
18. 18.A square garden has an area of 289 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 32 must be divided to get a perfect square?
20. 20.Which of these is a perfect square? (a) 289 (b) 321 (c) 302
21. 21.Which of these is a perfect square? (a) 484 (b) 488 (c) 508
22. 22.What is √4225? =
23. 23.What is the smallest whole number by which 343 must be divided to get a perfect square?
24. 24.How many whole numbers lie between 21² and 22²?
25. 25.What is √361? =
26. 26.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
27. 27.What is √7056? =
28. 28.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
29. 29.How many whole numbers lie between 44² and 45²?
30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
32. 32.A square garden has an area of 625 square m. How long is each side (in m)?
33. 33.What is the smallest whole number by which 175 must be divided to get a perfect square?
34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 33² and 34²?
36. 36.A square garden has an area of 900 square m. How long is each side (in m)?
37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 90 must be divided to get a perfect square?
39. 39.What is the smallest whole number by which 50 must be divided to get a perfect square?
40. 40.Which of these is a perfect square? (a) 324 (b) 348 (c) 338

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