Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 126 · 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.Which of these is a perfect square? (a) 1369 (b) 1413 (c) 1391
2. 2.What is 53²? =
3. 3.What is the smallest whole number by which 325 must be divided to get a perfect square?
4. 4.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √7225? =
7. 7.A square garden has an area of 289 square m. How long is each side (in m)?
8. 8.What is 92²? =
9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
10. 10.Which of these is a perfect square? (a) 961 (b) 1009 (c) 1008
11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
12. 12.A square garden has an area of 1936 square m. How long is each side (in m)?
13. 13.What is 21²? =
14. 14.How many whole numbers lie between 49² and 50²?
15. 15.What is 78²? =
16. 16.What is 16²? =
17. 17.A square garden has an area of 324 square m. How long is each side (in m)?
18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √7056? =
21. 21.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
22. 22.Which of these is a perfect square? (a) 397 (b) 382 (c) 361
23. 23.A square garden has an area of 2916 square m. How long is each side (in m)?
24. 24.What is √676? =
25. 25.What is √1296? =
26. 26.How many whole numbers lie between 38² and 39²?
27. 27.How many whole numbers lie between 33² and 34²?
28. 28.What is the smallest whole number by which 891 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
30. 30.A square garden has an area of 36 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 145 (b) 144 (c) 147
32. 32.What is √1681? =
33. 33.A square garden has an area of 121 square m. How long is each side (in m)?
34. 34.A square garden has an area of 256 square m. How long is each side (in m)?
35. 35.What is √2704? =
36. 36.What is the smallest whole number by which 224 must be divided to get a perfect square?
37. 37.What is 26²? =
38. 38.Which of these is a perfect square? (a) 316 (b) 295 (c) 289
39. 39.What is the smallest whole number by which 735 must be divided to get a perfect square?
40. 40.What is √9604? =

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