Products of Irrational Square Roots Practice

Question

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5 of 55 of 5 Items

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:

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