Question

Simplify each expression.

Radical Expressions

Answer 1

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Explanation:

Answer 2

`\frac{\sqrt[8]{2} }{\sqrt[2]{8} } = \frac{1}{\sqrt[8]{2^(11) } }`

`\sqrt{(5)/(7) } *\sqrt{(2)/(5) } =\sqrt{(2)/(7) }`

Explanation:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.