What is the product of cbrt(9) * sqrt(3) in simplest radical form?

What is the product of cbrt(9) * sqrt(3) in simplest radical form?

• A. 3*(6th root of 3)
• B. 3*(3rd root of 3)
• C. 9*(square root of 3)
• D. 3*(2nd root of 3)

Answer: (A)

To find the product of \( \sqrt[3]{9} \) and \( \sqrt{3} \) in simplest radical form, we first express both terms using exponents. The cube root of 9 can be rewritten as: \[ \sqrt[3]{9} = \sqrt[3]{3^2} = 3^{2/3} \] The square root of 3 can be expressed as: \[ \sqrt{3} = 3^{1/2} \] Now, we multiply the two expressions together: \[ \sqrt[3]{9} \cdot \sqrt{3} = 3^{2/3} \cdot 3^{1/2} \] When multiplying like bases, we add the exponents: \[ 3^{2/3 + 1/2} \] To add \( \frac{2}{3} \) and \( \frac{1}{2} \), we need a common denominator. The least common multiple of 3 and 2 is 6, so we convert the fractions: \[ \frac{2}{3} = \frac{4}{6} \quad \text{

To find the product of ( \sqrt[3]{9} ) and ( \sqrt{3} ) in simplest radical form, we first express both terms using exponents.

The cube root of 9 can be rewritten as:

[

\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{2/3}

]

The square root of 3 can be expressed as:

[

\sqrt{3} = 3^{1/2}

]

Now, we multiply the two expressions together:

[

\sqrt[3]{9} \cdot \sqrt{3} = 3^{2/3} \cdot 3^{1/2}

]

When multiplying like bases, we add the exponents:

[

3^{2/3 + 1/2}

]

To add ( \frac{2}{3} ) and ( \frac{1}{2} ), we need a common denominator. The least common multiple of 3 and 2 is 6, so we convert the fractions:

[

\frac{2}{3} = \frac{4}{6} \quad \text{