Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 561 · 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 56²? =
2. 2.What is 19²? =
3. 3.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
6. 6.What is 13²? =
7. 7.How many whole numbers lie between 25² and 26²?
8. 8.Which of these is a perfect square? (a) 431 (b) 423 (c) 400
9. 9.How many whole numbers lie between 24² and 25²?
10. 10.What is √3364? =
11. 11.Which of these is a perfect square? (a) 169 (b) 190 (c) 173
12. 12.What is 26²? =
13. 13.What is the smallest whole number by which 320 must be divided to get a perfect square?
14. 14.A square garden has an area of 1681 square m. How long is each side (in m)?
15. 15.How many whole numbers lie between 46² and 47²?
16. 16.Which of these is a perfect square? (a) 1537 (b) 1521 (c) 1534
17. 17.A square garden has an area of 2601 square m. How long is each side (in m)?
18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √6400? =
20. 20.What is 62²? =
21. 21.What is √7569? =
22. 22.What is √1296? =
23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
26. 26.How many whole numbers lie between 22² and 23²?
27. 27.A square garden has an area of 841 square m. How long is each side (in m)?
28. 28.Which of these is a perfect square? (a) 212 (b) 220 (c) 196
29. 29.A square garden has an area of 441 square m. How long is each side (in m)?
30. 30.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
31. 31.What is 21²? =
32. 32.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
33. 33.What is 71²? =
34. 34.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 90²? =
36. 36.A square garden has an area of 289 square m. How long is each side (in m)?
37. 37.How many whole numbers lie between 21² and 22²?
38. 38.How many whole numbers lie between 32² and 33²?
39. 39.What is √3025? =
40. 40.What is 70²? =

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