Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 707 · 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 50²? =
2. 2.What is 28²? =
3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 23²? =
5. 5.A square garden has an area of 1600 square m. How long is each side (in m)?
6. 6.What is √5625? =
7. 7.What is √900? =
8. 8.What is 33²? =
9. 9.What is 73²? =
10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 130 (b) 121 (c) 132
12. 12.Which of these is a perfect square? (a) 1619 (b) 1638 (c) 1600
13. 13.A square garden has an area of 529 square m. How long is each side (in m)?
14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
16. 16.What is 14²? =
17. 17.Which of these is a perfect square? (a) 181 (b) 172 (c) 169
18. 18.What is √2601? =
19. 19.What is 97²? =
20. 20.A square garden has an area of 1521 square m. How long is each side (in m)?
21. 21.Which of these is a perfect square? (a) 256 (b) 260 (c) 273
22. 22.What is 90²? =
23. 23.What is √2209? =
24. 24.What is 77²? =
25. 25.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
26. 26.What is 37²? =
27. 27.A square garden has an area of 49 square m. How long is each side (in m)?
28. 28.What is 79²? =
29. 29.A square garden has an area of 2304 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 27² and 28²?
31. 31.What is the smallest whole number by which 539 must be divided to get a perfect square?
32. 32.What is the smallest whole number by which 50 must be divided to get a perfect square?
33. 33.Which of these is a perfect square? (a) 100 (b) 109 (c) 101
34. 34.What is √6724? =
35. 35.Which of these is a perfect square? (a) 617 (b) 613 (c) 576
36. 36.Which of these is a perfect square? (a) 324 (b) 333 (c) 339
37. 37.What is √1089? =
38. 38.What is the smallest whole number by which 12 must be divided to get a perfect square?
39. 39.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
40. 40.A square garden has an area of 1936 square m. How long is each side (in m)?

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