Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 148 · 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 486 must be multiplied to get a perfect square?
2. 2.A square garden has an area of 289 square m. How long is each side (in m)?
3. 3.What is √5041? =
4. 4.What is the smallest whole number by which 350 must be divided to get a perfect square?
5. 5.A square garden has an area of 121 square m. How long is each side (in m)?
6. 6.What is 89²? =
7. 7.How many whole numbers lie between 25² and 26²?
8. 8.What is 29²? =
9. 9.What is √4900? =
10. 10.What is 69²? =
11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 85²? =
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √9409? =
16. 16.A square garden has an area of 961 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 529 (b) 562 (c) 533
18. 18.A square garden has an area of 81 square m. How long is each side (in m)?
19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √6561? =
21. 21.Which of these is a perfect square? (a) 303 (b) 298 (c) 289
22. 22.A square garden has an area of 256 square m. How long is each side (in m)?
23. 23.What is 16²? =
24. 24.What is 17²? =
25. 25.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
26. 26.What is 12²? =
27. 27.What is √1444? =
28. 28.What is the smallest whole number by which 252 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
30. 30.A square garden has an area of 729 square m. How long is each side (in m)?
31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
32. 32.How many whole numbers lie between 23² and 24²?
33. 33.What is √4489? =
34. 34.What is 56²? =
35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 55²? =
37. 37.How many whole numbers lie between 30² and 31²?
38. 38.What is 14²? =
39. 39.A square garden has an area of 169 square m. How long is each side (in m)?
40. 40.What is √1681? =

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