Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 417 · 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 70²? =
2. 2.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
3. 3.A square garden has an area of 256 square m. How long is each side (in m)?
4. 4.How many whole numbers lie between 6² and 7²?
5. 5.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
6. 6.What is 39²? =
7. 7.What is 89²? =
8. 8.What is √2500? =
9. 9.What is 42²? =
10. 10.Which of these is a perfect square? (a) 1641 (b) 1600 (c) 1619
11. 11.What is √324? =
12. 12.What is √9216? =
13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 60²? =
15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
16. 16.A square garden has an area of 3364 square m. How long is each side (in m)?
17. 17.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 13² and 14²?
19. 19.A square garden has an area of 196 square m. How long is each side (in m)?
20. 20.What is 63²? =
21. 21.What is √6084? =
22. 22.What is 23²? =
23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
24. 24.What is 74²? =
25. 25.How many whole numbers lie between 48² and 49²?
26. 26.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
27. 27.Which of these is a perfect square? (a) 100 (b) 102 (c) 104
28. 28.Which of these is a perfect square? (a) 221 (b) 205 (c) 196
29. 29.A square garden has an area of 3481 square m. How long is each side (in m)?
30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 191 (b) 189 (c) 169
33. 33.What is the smallest whole number by which 540 must be divided to get a perfect square?
34. 34.What is √1681? =
35. 35.How many whole numbers lie between 37² and 38²?
36. 36.How many whole numbers lie between 18² and 19²?
37. 37.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
38. 38.What is √7225? =
39. 39.How many whole numbers lie between 41² and 42²?
40. 40.A square garden has an area of 841 square m. How long is each side (in m)?

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