Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 87 · 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 √5041? =
2. 2.Which of these is a perfect square? (a) 257 (b) 256 (c) 263
3. 3.How many whole numbers lie between 39² and 40²?
4. 4.What is 29²? =
5. 5.What is 30²? =
6. 6.Which of these is a perfect square? (a) 125 (b) 121 (c) 124
7. 7.A square garden has an area of 2601 square m. How long is each side (in m)?
8. 8.Which of these is a perfect square? (a) 665 (b) 625 (c) 643
9. 9.What is √441? =
10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √1444? =
12. 12.What is the smallest whole number by which 1134 must be divided to get a perfect square?
13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
14. 14.How many whole numbers lie between 20² and 21²?
15. 15.What is √2209? =
16. 16.What is 69²? =
17. 17.What is 15²? =
18. 18.How many whole numbers lie between 17² and 18²?
19. 19.What is the smallest whole number by which 250 must be divided to get a perfect square?
20. 20.What is √2601? =
21. 21.What is 93²? =
22. 22.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
23. 23.What is √169? =
24. 24.What is √6241? =
25. 25.What is √7225? =
26. 26.What is the smallest whole number by which 75 must be divided to get a perfect square?
27. 27.What is √1296? =
28. 28.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
29. 29.A square garden has an area of 3600 square m. How long is each side (in m)?
30. 30.A square garden has an area of 225 square m. How long is each side (in m)?
31. 31.How many whole numbers lie between 13² and 14²?
32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
34. 34.How many whole numbers lie between 18² and 19²?
35. 35.Which of these is a perfect square? (a) 927 (b) 949 (c) 900
36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 59²? =
38. 38.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √6561? =
40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?

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