Finite Math Examples

$\sqrt{y^{5}} \sqrt[3]{y^{8}}$

Step 1

Set the radicand in $\sqrt{y^{5}}$ less than $0$ to find where the expression is undefined.

$y^{5} < 0$

Step 2

Solve for $y$ .

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Step 2.1

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt[5]{y^{5}} < \sqrt[5]{0}$

Step 2.2

Simplify the equation.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Pull terms out from under the radical.

$y < \sqrt[5]{0}$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $\sqrt[5]{0}$ .

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Step 2.2.2.1.1

Rewrite $0$ as $0^{5}$ .

$y < \sqrt[5]{0^{5}}$

Step 2.2.2.1.2

Pull terms out from under the radical.

$y < 0$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$y < 0$

$(- \infty, 0)$

Step 4