Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 667 · 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 128 must be multiplied to get a perfect square?
2. 2.What is 69²? =
3. 3.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
4. 4.How many whole numbers lie between 39² and 40²?
5. 5.What is 55²? =
6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
7. 7.How many whole numbers lie between 30² and 31²?
8. 8.What is 59²? =
9. 9.Which of these is a perfect square? (a) 854 (b) 841 (c) 897
10. 10.What is the smallest whole number by which 98 must be divided to get a perfect square?
11. 11.What is the smallest whole number by which 52 must be divided to get a perfect square?
12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 9² and 10²?
14. 14.What is √784? =
15. 15.A square garden has an area of 1024 square m. How long is each side (in m)?
16. 16.What is 57²? =
17. 17.What is √6241? =
18. 18.A square garden has an area of 2704 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
20. 20.What is √5476? =
21. 21.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
22. 22.What is √9801? =
23. 23.What is 35²? =
24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
26. 26.What is 19²? =
27. 27.What is 53²? =
28. 28.What is 26²? =
29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
32. 32.A square garden has an area of 1225 square m. How long is each side (in m)?
33. 33.What is 73²? =
34. 34.What is 93²? =
35. 35.Which of these is a perfect square? (a) 749 (b) 729 (c) 748
36. 36.What is 95²? =
37. 37.What is 23²? =
38. 38.What is 62²? =
39. 39.A square garden has an area of 36 square m. How long is each side (in m)?
40. 40.What is √1089? =

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