Question

What is the following product? ^3sqrt 24 * ^3sqrt 45

Answer 1

`6\sqrt[3]{5}`

Explanation:

`\sqrt[3]{24}` *
`\sqrt[3]{45}`

Simplify each expression if possible

(Find a cubed number which can be multiplied to make 24/45. In this case, we can only make 24 buy multiplying 3 and 8. 8 =
`2^(3)`.

`\sqrt[3]{24} = \sqrt[3]{3 * 8} = 2*\sqrt[3]{3}` = 2\sqrt[3]{3}[/tex]

Substitute this into the equation.

`2\sqrt[3]{3}*\sqrt[3]{45} = 2\sqrt[3]{3*45} = 2\sqrt[3]{135}`

Simplify each expression if possible

(Find a cubed number which can be multiplied to make 135. We can make this buy multiplying 5 and 27. 27 =
`3^(3)`.

`2\sqrt[3]{135} = 2\sqrt[3]{5 * 27} = 2*3\sqrt[3]{5} = 6\sqrt[3]{5}`

Answer 2

295.77

Explanation:

Solution :

^3sqrt 24 * ^3sqrt 45

∛24 * ∛45 =295.77