Products of Irrational Square Roots Practice

Question

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Question
What is ^3√−72
simplified?

Note: You will find the option to add a cubic root symbol in the Algebra (×)
keyboard.

(1 point)
Remaining Attempts : 3

Answer 1

To simplify the expression \(\sqrt[3]{-72}\), you can factor \(-72\) into its prime factors.

\[ -72 = -1 \times 2^3 \times 3^2 \]

Now, apply the cubic root:

\[ \sqrt[3]{-72} = \sqrt[3]{-1 \times 2^3 \times 3^2} \]

Breaking it down further:

\[ \sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{3^2} \]

Calculating each term, we get:

• \(\sqrt[3]{-1} = -1\)
• \(\sqrt[3]{2^3} = 2\)
• \(\sqrt[3]{3^2} = \sqrt[3]{9}\) (this cannot be simplified further)

Putting it all together:

\[ \sqrt[3]{-72} = -1 \times 2 \times \sqrt[3]{9} = -2\sqrt[3]{9} \]

So, the simplified form of \(\sqrt[3]{-72}\) is:

\[ -2\sqrt[3]{9} \]