Question

What is the following product 3 square root 16 x7 times3 square root 12 x9

Answer 1

`4x^5\sqrt[3]{3x}`

Explanation:

The product will be written as:

`\sqrt[3]{16x^7}*\sqrt[3]{12x^9}`

As both the radicals have same root 3 so,

`= \sqrt[3]{16x^7 * 12x^9}`

The powers of x will be added as the base is same

`=\sqrt[3]{16*12 * x^((7+9))}\\=\sqrt[3]{192x^(16)}\\`

We have to break the terms so that the powers can be written as a multiple of 3

`=\sqrt[3]{64*3*x^(15)*x}\\ =\sqrt[3]{(4^3)*3*(x^(3*5))*x}\\ Applying\ cube\ root\\= 4x^5\sqrt[3]{3x}`