Question

3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.81​

Answer 1

Answer:

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Step-by-step explanation:

first you need to divide 81 by divison method then see which pair is two or 1 there is 1 three so we have to divide it by 3

Answer 2

Prime factors of 81 = 3 x 3 x 3 x 3

Here one factor 3 is not grouped in triplets.

Therefore 81 must be divided by 3 to make it a perfect cube.

(ii) 128

Prime factors of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 must be divided by 2 to make it a perfect cube.

(iii) 135

Prime factors of 135 = 3 x 3 x 3 x 5

Here one factor 5 does not appear in a triplet.

Therefore, 135 must be divided by 5 to make it a perfect cube.

(iv) 192

Prime factors of 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Here one factor 3 does not appear in a triplet.

Therefore, 192 must be divided by 3 to make it a perfect cube.

(v) 704

Prime factors of 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

Here one factor 11 does not appear in a triplet.

Therefore, 704 must be divided by 11 to make it a perfect cube.