Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 378 · 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 √3136? =
2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 28²? =
4. 4.A square garden has an area of 441 square m. How long is each side (in m)?
5. 5.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
6. 6.Which of these is a perfect square? (a) 529 (b) 552 (c) 554
7. 7.How many whole numbers lie between 19² and 20²?
8. 8.How many whole numbers lie between 28² and 29²?
9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 81²? =
11. 11.A square garden has an area of 81 square m. How long is each side (in m)?
12. 12.A square garden has an area of 121 square m. How long is each side (in m)?
13. 13.What is 53²? =
14. 14.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
15. 15.Which of these is a perfect square? (a) 1175 (b) 1204 (c) 1156
16. 16.What is the smallest whole number by which 18 must be divided to get a perfect square?
17. 17.A square garden has an area of 3249 square m. How long is each side (in m)?
18. 18.A square garden has an area of 25 square m. How long is each side (in m)?
19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √1156? =
21. 21.What is 42²? =
22. 22.Which of these is a perfect square? (a) 625 (b) 646 (c) 653
23. 23.How many whole numbers lie between 5² and 6²?
24. 24.What is 25²? =
25. 25.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
26. 26.What is √625? =
27. 27.What is 92²? =
28. 28.What is √729? =
29. 29.Which of these is a perfect square? (a) 250 (b) 228 (c) 225
30. 30.How many whole numbers lie between 50² and 51²?
31. 31.Which of these is a perfect square? (a) 1225 (b) 1263 (c) 1232
32. 32.A square garden has an area of 324 square m. How long is each side (in m)?
33. 33.What is the smallest whole number by which 192 must be divided to get a perfect square?
34. 34.Which of these is a perfect square? (a) 1313 (b) 1315 (c) 1296
35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 51²? =
37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
38. 38.A square garden has an area of 1600 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 162 (b) 144 (c) 145
40. 40.A square garden has an area of 841 square m. How long is each side (in m)?

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