Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 486 · 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 sum of the first 9 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 729 square m. How long is each side (in m)?
3. 3.Which of these is a perfect square? (a) 1538 (b) 1521 (c) 1592
4. 4.How many whole numbers lie between 34² and 35²?
5. 5.What is √2704? =
6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 15²? =
8. 8.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
9. 9.Which of these is a perfect square? (a) 496 (b) 484 (c) 494
10. 10.What is the smallest whole number by which 150 must be divided to get a perfect square?
11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 80 must be divided to get a perfect square?
13. 13.How many whole numbers lie between 21² and 22²?
14. 14.What is the smallest whole number by which 50 must be divided to get a perfect square?
15. 15.What is 20²? =
16. 16.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
17. 17.What is √7569? =
18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 174 (b) 169 (c) 178
21. 21.What is √1225? =
22. 22.Which of these is a perfect square? (a) 225 (b) 235 (c) 247
23. 23.What is √529? =
24. 24.How many whole numbers lie between 18² and 19²?
25. 25.A square garden has an area of 49 square m. How long is each side (in m)?
26. 26.What is √2916? =
27. 27.What is √8281? =
28. 28.A square garden has an area of 2500 square m. How long is each side (in m)?
29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √9604? =
31. 31.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
33. 33.What is 45²? =
34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
36. 36.What is √3600? =
37. 37.Which of these is a perfect square? (a) 209 (b) 196 (c) 199
38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
40. 40.What is the smallest whole number by which 275 must be multiplied to get a perfect square?

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