Question

Simplify each cube root expression. Describe the simplified form of the expression as rational or irrational. In your final answer, include all of your work.
3 square root of 81


3 square root of -64

Answer 1

Answer:

• $\sqrt[3]{81}=3\sqrt[3]{3}$
• $\sqrt[3]{-64}=-4$

Step-by-step explanation:

a)

$\sqrt[3]{81}=\sqrt[3]{3^4}=\sqrt[3]{(3^3)(3)}=3\sqrt[3]{3}$

This is irrational.

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b)

$\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4$

This is rational.

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Please be aware that 3 square root of 81 is not the same as cube root of 81.

$3\sqrt{81}\ne\sqrt[3]{81}$

You can call a cube root what it is.