Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 723 · 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 23²? =
2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
3. 3.What is √1296? =
4. 4.What is the smallest whole number by which 396 must be divided to get a perfect square?
5. 5.What is the smallest whole number by which 448 must be divided to get a perfect square?
6. 6.Which of these is a perfect square? (a) 268 (b) 265 (c) 256
7. 7.A square garden has an area of 400 square m. How long is each side (in m)?
8. 8.How many whole numbers lie between 14² and 15²?
9. 9.What is 72²? =
10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 42²? =
13. 13.A square garden has an area of 196 square m. How long is each side (in m)?
14. 14.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √484? =
17. 17.Which of these is a perfect square? (a) 100 (b) 104 (c) 105
18. 18.A square garden has an area of 100 square m. How long is each side (in m)?
19. 19.A square garden has an area of 121 square m. How long is each side (in m)?
20. 20.What is the smallest whole number by which 540 must be divided to get a perfect square?
21. 21.What is √900? =
22. 22.A square garden has an area of 81 square m. How long is each side (in m)?
23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √256? =
25. 25.What is 45²? =
26. 26.A square garden has an area of 1764 square m. How long is each side (in m)?
27. 27.Which of these is a perfect square? (a) 336 (b) 343 (c) 324
28. 28.What is √169? =
29. 29.What is 80²? =
30. 30.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
31. 31.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
33. 33.What is the smallest whole number by which 63 must be divided to get a perfect square?
34. 34.Which of these is a perfect square? (a) 121 (b) 134 (c) 125
35. 35.What is √7396? =
36. 36.Which of these is a perfect square? (a) 1403 (b) 1443 (c) 1369
37. 37.What is √3136? =
38. 38.How many whole numbers lie between 49² and 50²?
39. 39.What is √1444? =
40. 40.How many whole numbers lie between 20² and 21²?

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