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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 :

sqdancefan

Answer:

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

Step-by-step explanation:

a)

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

This is irrational.

__

b)

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

This is rational.

_____

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

[tex]3\sqrt{81}\ne\sqrt[3]{81}[/tex]

You can call a cube root what it is.

Josiahohara11

Answer:

3 square root of 81 is irrational

3 square root of -64 is rational

Step-by-step explanation:

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