Question

Which is the smallest three-digit perfect cube?

(a) 125 (b) 343 (c) 729 (d) 512
​

Answer 1

(a) 125

The smallest three digit perfect cube is 125.

Step-by-step explanation:

Let us check why the given numbers are perfect cube first and then find the smallest of them.

• 125 = 5 × 5 × 5 = 5³, and thus 125 is a perfect cube.

• 343 = 7 × 7 × 7 = 7³, and thus 343 is a perfect cube.

• 729 = 9 × 9 × 9 = 9³, and thus 729 is a perfect cube.

• 512 = 8 × 8 × 8 = 8³, and thus 512 is a perfect cube.

Here, we see that all the given numbers are perfect cube.

However, 125 < 343 < 512 < 729.

Thus 125 is the smallest three digit perfect cube.

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Answer 2

According the question, we have to find out the smallest three-digit perfect cube.

Given numbers are stated bellow:-

1. 125 = 5×5×5 = 5³,
2. 343 = 7×7×7 =7³
3. 729 = 9×9×9 =9³
4. 512= 8×8×8 =8³

Hence  125 is a perfect cube of 5. ( 5³ =125)

             343 is a perfect cube of 7. ( 7³ =343)

              729 is a perfect cube of 9. ( 9³ = 729)

             512 is a perfect cube of 8. ( 8³ = 512).

Here we can see that , , 125 < 343 < 512 < 729.

∴  125 is the smallest three digit perfect cube.

Ans :-  125 is the smallest three digit perfect cube.

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