Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 335 · 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 12 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 1225 square m. How long is each side (in m)?
3. 3.What is 73²? =
4. 4.What is 20²? =
5. 5.A square garden has an area of 36 square m. How long is each side (in m)?
6. 6.A square garden has an area of 1296 square m. How long is each side (in m)?
7. 7.A square garden has an area of 144 square m. How long is each side (in m)?
8. 8.A square garden has an area of 841 square m. How long is each side (in m)?
9. 9.Which of these is a perfect square? (a) 797 (b) 801 (c) 784
10. 10.How many whole numbers lie between 28² and 29²?
11. 11.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
12. 12.Which of these is a perfect square? (a) 1444 (b) 1515 (c) 1489
13. 13.What is the smallest whole number by which 80 must be divided to get a perfect square?
14. 14.Which of these is a perfect square? (a) 729 (b) 760 (c) 746
15. 15.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
16. 16.Which of these is a perfect square? (a) 1009 (b) 961 (c) 1014
17. 17.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the smallest whole number by which 891 must be divided to get a perfect square?
20. 20.How many whole numbers lie between 42² and 43²?
21. 21.What is √900? =
22. 22.What is 56²? =
23. 23.How many whole numbers lie between 21² and 22²?
24. 24.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 13² and 14²?
26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the smallest whole number by which 468 must be divided to get a perfect square?
28. 28.What is 19²? =
29. 29.A square garden has an area of 196 square m. How long is each side (in m)?
30. 30.Which of these is a perfect square? (a) 631 (b) 625 (c) 626
31. 31.What is the smallest whole number by which 60 must be divided to get a perfect square?
32. 32.What is 35²? =
33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 490 must be divided to get a perfect square?
35. 35.What is √1369? =
36. 36.How many whole numbers lie between 18² and 19²?
37. 37.How many whole numbers lie between 22² and 23²?
38. 38.What is 44²? =
39. 39.A square garden has an area of 324 square m. How long is each side (in m)?
40. 40.What is √6724? =

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