Finite Math Examples

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

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

Step 1

Set the radicand in

\sqrt{y^{5}}

$\sqrt{y^{5}}$ less than

0

$0$ to find where the expression is undefined.

y^{5} < 0

$y^{5} < 0$

Step 2

Solve for

y

$y$ .

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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}

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

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}

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

y < \sqrt[5]{0}

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

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify

\sqrt[5]{0}

$\sqrt[5]{0}$ .

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Step 2.2.2.1.1

Rewrite

0

$0$ as

0^{5}

$0^{5}$ .

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

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

Step 2.2.2.1.2

Pull terms out from under the radical.

y < 0

$y < 0$

y < 0

$y < 0$

y < 0

$y < 0$

y < 0

$y < 0$

y < 0

$y < 0$

Step 3

The equation is undefined where the denominator equals

0

$0$ , the argument of a square root is less than

0

$0$ , or the argument of a logarithm is less than or equal to

0

$0$ .

y < 0

$y < 0$

(- \infty, 0)

$(- \infty, 0)$

Step 4