Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 517 · 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 490 must be multiplied to get a perfect square?
2. 2.What is √8281? =
3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 576 square m. How long is each side (in m)?
6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √7396? =
8. 8.What is 83²? =
9. 9.How many whole numbers lie between 14² and 15²?
10. 10.What is √2809? =
11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
12. 12.What is √3136? =
13. 13.What is √1369? =
14. 14.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 85²? =
16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
17. 17.How many whole numbers lie between 6² and 7²?
18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
19. 19.A square garden has an area of 484 square m. How long is each side (in m)?
20. 20.A square garden has an area of 3025 square m. How long is each side (in m)?
21. 21.What is √3969? =
22. 22.How many whole numbers lie between 38² and 39²?
23. 23.What is 54²? =
24. 24.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
26. 26.A square garden has an area of 1225 square m. How long is each side (in m)?
27. 27.What is 70²? =
28. 28.What is 78²? =
29. 29.What is √961? =
30. 30.Which of these is a perfect square? (a) 1225 (b) 1229 (c) 1226
31. 31.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
33. 33.What is 90²? =
34. 34.What is √1156? =
35. 35.What is 45²? =
36. 36.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
37. 37.What is 75²? =
38. 38.How many whole numbers lie between 49² and 50²?
39. 39.What is 31²? =
40. 40.A square garden has an area of 2916 square m. How long is each side (in m)?

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