Question

find the smallest number by which 200 should be multiplied to make it a perfect cube​

Answer 1

Answer:

The factors of 200 are 2×2×2×5×5

Step-by-step explanation:

Therefore 5 is the required number to make a perfect cube .

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Answer 2

The smallest number is 5

Step-by-step explanation:

We have to find the smallest number by which 200 should be multiplied to make it a perfect cube.

Now, 200

= 2 × 2 × 2 × 5 × 5

= 2³ × 5²

We see that though the exponent of 2 is 3, the exponent of 5 is 2. In order to find the perfect cube, the exponent of 5 must be 3.

Thus we multiply 200 by 5.

Then 200 * 5

= 1000

= 10³, a perfect cube

∴ the required smallest number is 5.