Which of the following numbers is a perfect cube?
a. 243
b. 216
c. 392
d. 8640
Solution:
We have to find the number which is a perfect cube.
Number obtained when a number is multiplied by itself three times is called a cube number.
If m = n³, then m is a perfect cube where m and n are natural numbers.
Considering 243,
243 = 3 × 3 × 3 × 3 × 3
We observe that 3 × 3 do not occur in pairs.
Therefore, 243 is not a perfect cube.
Considering 216,
By prime factorisation,
216 = 2 × 2 × 2 × 3 × 3 × 3
Therefore, 216 is a perfect cube.
Considering 392,
By prime factorisation,
392 = 2 × 2 × 2 × 7 × 7
We observe that 7 × 7 do not occur in pairs.
Therefore, 392 is not a perfect cube.
Considering 8640,
By prime factorisation,
8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
We observe that 5 does not occur in pairs.
Therefore, 8640 is not a perfect cube.
✦ Try This: Which of the following numbers is a perfect cube? a. 224, b. 1331, c. 398, d. 8642
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 13
Which of the following numbers is a perfect cube? a. 243, b. 216, c. 392, d. 8640
Summary:
216 is a perfect cube
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