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

3 square root of 81 is irrational

3 square root of -64 is rational

Explanation:

Answer 2

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

Explanation:

a)

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

This is irrational.

__

b)

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

This is rational.

_____

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

`3√(81)\\e\sqrt[3]{81}`

You can call a cube root what it is.