Trigonometry Examples

$3 \sqrt{p^{5} + 6}$

Step 1

Set the radicand in $\sqrt{p^{5} + 6}$ less than $0$ to find where the expression is undefined.

$p^{5} + 6 < 0$

Step 2

Solve for $p$ .

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Step 2.1

Subtract $6$ from both sides of the inequality.

$p^{5} < - 6$

Step 2.2

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

$\sqrt[5]{p^{5}} < \sqrt[5]{- 6}$

Step 2.3

Simplify the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Pull terms out from under the radical.

$p < \sqrt[5]{- 6}$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\sqrt[5]{- 6}$ .

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Step 2.3.2.1.1

Rewrite $- 6$ as ${(- 1)}^{5} \cdot 6$ .

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Step 2.3.2.1.1.1

Rewrite $- 6$ as $- 1 (6)$ .

$p < \sqrt[5]{- 1 (6)}$

Step 2.3.2.1.1.2

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$p < \sqrt[5]{{(- 1)}^{5} \cdot 6}$

Step 2.3.2.1.2

Pull terms out from under the radical.

$p < - 1 \sqrt[5]{6}$

Step 2.3.2.1.3

Rewrite $- 1 \sqrt[5]{6}$ as $- \sqrt[5]{6}$ .

$p < - \sqrt[5]{6}$

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 $0$ .

$p < - \sqrt[5]{6}$

$(- \infty, - \sqrt[5]{6})$

Step 4