Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 159 · 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 147 must be divided to get a perfect square?
2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
3. 3.Which of these is a perfect square? (a) 1171 (b) 1202 (c) 1156
4. 4.What is √576? =
5. 5.What is 81²? =
6. 6.What is √2209? =
7. 7.What is the smallest whole number by which 180 must be divided to get a perfect square?
8. 8.What is √1024? =
9. 9.Which of these is a perfect square? (a) 144 (b) 147 (c) 150
10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 554 (b) 529 (c) 538
12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 900 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 900 (b) 918 (c) 902
15. 15.A square garden has an area of 225 square m. How long is each side (in m)?
16. 16.What is 60²? =
17. 17.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √676? =
20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 810 must be divided to get a perfect square?
22. 22.A square garden has an area of 144 square m. How long is each side (in m)?
23. 23.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
24. 24.What is √2500? =
25. 25.A square garden has an area of 2209 square m. How long is each side (in m)?
26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
28. 28.A square garden has an area of 361 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 125 (b) 136 (c) 121
30. 30.What is 68²? =
31. 31.What is 90²? =
32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
33. 33.How many whole numbers lie between 19² and 20²?
34. 34.How many whole numbers lie between 31² and 32²?
35. 35.Which of these is a perfect square? (a) 1600 (b) 1654 (c) 1663
36. 36.What is 34²? =
37. 37.What is 14²? =
38. 38.What is 44²? =
39. 39.A square garden has an area of 49 square m. How long is each side (in m)?
40. 40.What is 69²? =

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