The number 137592 is not a perfect cube. Its prime factorisation is 137592 = 2^3 x 3^4 x 7^3. Find the smallest number it must be divided by to give a perfect cube, and the cube root of the result.

Question

Accepted Answer

divide by 3, cube root 42. 137592 = 2^3 x 3^4 x 7^3. The 3 has exponent 4; remove one 3 (divide by 3) to leave 3^3. Result = 2^3 x 3^3 x 7^3 = (2 x 3 x 7)^3 = 42^3, cube root = 42.

The number 137592 is not a perfect cube.
Its prime factorisation is $137592 = 2^{3} \times 3^{4} \times 7^{3}$ .
Find the smallest number it must be divided by to give a perfect cube, and the cube root of the result.

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More Class 8 Cube Root by Prime Factorisation practice

The number 137592 is not a perfect cube.Its prime factorisation is 137592=23×34×73.Find the smallest number it must be divided by to give a perfect cube, and the cube root of the result.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Cube Root by Prime Factorisation practice

The number 137592 is not a perfect cube.
Its prime factorisation is $137592 = 2^{3} \times 3^{4} \times 7^{3}$ .
Find the smallest number it must be divided by to give a perfect cube, and the cube root of the result.