Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 500 · 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 50 must be multiplied to get a perfect square?
2. 2.What is √1089? =
3. 3.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
4. 4.How many whole numbers lie between 28² and 29²?
5. 5.What is 78²? =
6. 6.What is 91²? =
7. 7.What is √6561? =
8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 94²? =
10. 10.What is the smallest whole number by which 45 must be divided to get a perfect square?
11. 11.How many whole numbers lie between 20² and 21²?
12. 12.A square garden has an area of 3600 square m. How long is each side (in m)?
13. 13.How many whole numbers lie between 37² and 38²?
14. 14.How many whole numbers lie between 35² and 36²?
15. 15.How many whole numbers lie between 12² and 13²?
16. 16.What is the smallest whole number by which 384 must be divided to get a perfect square?
17. 17.What is 52²? =
18. 18.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
19. 19.What is √256? =
20. 20.Which of these is a perfect square? (a) 282 (b) 256 (c) 273
21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √729? =
24. 24.A square garden has an area of 400 square m. How long is each side (in m)?
25. 25.How many whole numbers lie between 13² and 14²?
26. 26.What is 18²? =
27. 27.What is 72²? =
28. 28.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
29. 29.What is 75²? =
30. 30.A square garden has an area of 1521 square m. How long is each side (in m)?
31. 31.What is 88²? =
32. 32.What is 25²? =
33. 33.What is √3136? =
34. 34.What is 30²? =
35. 35.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
36. 36.What is √676? =
37. 37.What is 22²? =
38. 38.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
39. 39.A square garden has an area of 841 square m. How long is each side (in m)?
40. 40.What is √4489? =

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