Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 178 · 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.Which of these is a perfect square? (a) 194 (b) 193 (c) 169
2. 2.What is the smallest whole number by which 448 must be divided to get a perfect square?
3. 3.What is 94²? =
4. 4.How many whole numbers lie between 20² and 21²?
5. 5.What is √3844? =
6. 6.Which of these is a perfect square? (a) 1527 (b) 1521 (c) 1523
7. 7.Which of these is a perfect square? (a) 914 (b) 943 (c) 900
8. 8.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
9. 9.A square garden has an area of 225 square m. How long is each side (in m)?
10. 10.A square garden has an area of 3364 square m. How long is each side (in m)?
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.How many whole numbers lie between 30² and 31²?
13. 13.What is the smallest whole number by which 180 must be divided to get a perfect square?
14. 14.What is √144? =
15. 15.A square garden has an area of 961 square m. How long is each side (in m)?
16. 16.A square garden has an area of 3025 square m. How long is each side (in m)?
17. 17.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 18²? =
20. 20.Which of these is a perfect square? (a) 223 (b) 213 (c) 196
21. 21.What is the smallest whole number by which 90 must be divided to get a perfect square?
22. 22.What is 74²? =
23. 23.What is 86²? =
24. 24.What is 54²? =
25. 25.What is 70²? =
26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
27. 27.What is 20²? =
28. 28.A square garden has an area of 2209 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
30. 30.What is 61²? =
31. 31.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
33. 33.What is 46²? =
34. 34.Which of these is a perfect square? (a) 160 (b) 161 (c) 144
35. 35.What is √484? =
36. 36.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
37. 37.What is the smallest whole number by which 96 must be divided to get a perfect square?
38. 38.What is 75²? =
39. 39.What is √1681? =
40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?

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