Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 612 · 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 637 must be multiplied to get a perfect square?
2. 2.Which of these is a perfect square? (a) 545 (b) 529 (c) 565
3. 3.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
4. 4.What is 88²? =
5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 39²? =
7. 7.A square garden has an area of 3600 square m. How long is each side (in m)?
8. 8.What is 55²? =
9. 9.What is 34²? =
10. 10.How many whole numbers lie between 35² and 36²?
11. 11.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 155 (b) 144 (c) 152
14. 14.A square garden has an area of 2601 square m. How long is each side (in m)?
15. 15.Which of these is a perfect square? (a) 256 (b) 262 (c) 273
16. 16.Which of these is a perfect square? (a) 1296 (b) 1360 (c) 1328
17. 17.A square garden has an area of 961 square m. How long is each side (in m)?
18. 18.What is 25²? =
19. 19.A square garden has an area of 196 square m. How long is each side (in m)?
20. 20.What is 53²? =
21. 21.What is √144? =
22. 22.Which of these is a perfect square? (a) 1026 (b) 1063 (c) 1024
23. 23.What is 36²? =
24. 24.What is the smallest whole number by which 325 must be divided to get a perfect square?
25. 25.What is √7744? =
26. 26.What is √625? =
27. 27.What is 38²? =
28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 1222 (b) 1156 (c) 1224
30. 30.What is √1369? =
31. 31.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 18 must be divided to get a perfect square?
33. 33.How many whole numbers lie between 25² and 26²?
34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
35. 35.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
36. 36.A square garden has an area of 100 square m. How long is each side (in m)?
37. 37.What is 22²? =
38. 38.What is √4489? =
39. 39.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
40. 40.What is 98²? =

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