Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 659 · 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 10 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 69²? =
3. 3.What is 63²? =
4. 4.What is 25²? =
5. 5.What is 75²? =
6. 6.How many whole numbers lie between 48² and 49²?
7. 7.What is 86²? =
8. 8.What is √4761? =
9. 9.What is the smallest whole number by which 250 must be divided to get a perfect square?
10. 10.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
11. 11.What is √729? =
12. 12.What is the smallest whole number by which 180 must be divided to get a perfect square?
13. 13.What is 52²? =
14. 14.What is √1936? =
15. 15.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √8281? =
17. 17.What is √6400? =
18. 18.Which of these is a perfect square? (a) 256 (b) 279 (c) 257
19. 19.A square garden has an area of 256 square m. How long is each side (in m)?
20. 20.Which of these is a perfect square? (a) 1634 (b) 1600 (c) 1617
21. 21.A square garden has an area of 2500 square m. How long is each side (in m)?
22. 22.How many whole numbers lie between 13² and 14²?
23. 23.What is the smallest whole number by which 320 must be divided to get a perfect square?
24. 24.What is 54²? =
25. 25.Which of these is a perfect square? (a) 867 (b) 841 (c) 865
26. 26.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √2025? =
28. 28.A square garden has an area of 2704 square m. How long is each side (in m)?
29. 29.A square garden has an area of 3249 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 37² and 38²?
31. 31.What is 11²? =
32. 32.A square garden has an area of 49 square m. How long is each side (in m)?
33. 33.What is 29²? =
34. 34.A square garden has an area of 841 square m. How long is each side (in m)?
35. 35.What is 37²? =
36. 36.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
37. 37.Which of these is a perfect square? (a) 170 (b) 173 (c) 169
38. 38.A square garden has an area of 900 square m. How long is each side (in m)?
39. 39.What is 71²? =
40. 40.What is the smallest whole number by which 325 must be divided to get a perfect square?

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets