Linear Algebra Examples

$\sqrt{59 x^{9}}$

Step 1

Set the radicand in $\sqrt{59 x^{9}}$ greater than or equal to $0$ to find where the expression is defined.

$59 x^{9} \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $59 x^{9} \geq 0$ by $59$ and simplify.

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Step 2.1.1

Divide each term in $59 x^{9} \geq 0$ by $59$ .

$\frac{59 x^{9}}{59} \geq \frac{0}{59}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $59$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{59 x^{9}}{59} \geq \frac{0}{59}$

Step 2.1.2.1.2

Divide $x^{9}$ by $1$ .

$x^{9} \geq \frac{0}{59}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $59$ .

$x^{9} \geq 0$

Step 2.2

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

$\sqrt[9]{x^{9}} \geq \sqrt[9]{0}$

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.

$x \geq \sqrt[9]{0}$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\sqrt[9]{0}$ .

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Step 2.3.2.1.1

Rewrite $0$ as $0^{9}$ .

$x \geq \sqrt[9]{0^{9}}$

Step 2.3.2.1.2

Pull terms out from under the radical.

$x \geq 0$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4