Question

The expression cube root of 54x^8y^12 can be written in simplest radical form as

Answer 1

Answer:

The simplest radical form of the cubic root is $3x^2y^4\sqrt[3]{2x}$

Step-by-step explanation:

Cube root of 54x^8y^12

That is:

$\sqrt[3]{54x^8y^12}$

Can be simplified as:

$\sqrt[3]{54x^8y^12} = \sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12}$

We find each separate simplification, and multiply them:

Cubic root of 54:

$54 = 2*3^3$

So

$\sqrt[3]{54} = \sqrt[3]{2*3^3} = 3\sqrt[3]{2}$

Cubic root of x^8

$\sqrt[3]{x^8} = \sqrt[3]{x^6*x^2} = x^2\sqrt[3]{x^2}$

Cubic root of y^12

$\sqrt[3]{y^{12}} = y^4$

Multiplying all these terms:

$\sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12} = 3\sqrt[3]{2}(x^2\sqrt[3]{x^2})(y^4) = 3x^2y^4\sqrt[3]{2x}$

The simplest radical form of the cubic root is $3x^2y^4\sqrt[3]{2x}$