Question

Find the cube root. How do I break down 1728 to easily find the cube root?

Answer 1

Given:

`\sqrt[3]{1728}`

Aim:

We need to find the cube root of 1728.

Step-by-step explanation:

Consider the prime factors of the number 1728.

`1728=2*2*2*2*2*2*3*3*3`

`1728=(2*2*2)*(2*2*2)*(3*3*3)`

`1728=2^3*2^3*3^3`

`1728=(2*2*3)^3`

`1728=12^3`

Take cube root on both sides.

`\sqrt[3]{1728}=\sqrt[3]{12^3}`

`\sqrt[3]{1728}=12`

Final answer:

`\sqrt[3]{1728}=12`