Linear Algebra Examples

$2 \sqrt{8 x} x \sqrt{8 x^{2}}$

Step 1

Set the radicand in $\sqrt{8 x}$ greater than or equal to $0$ to find where the expression is defined.

$8 x \geq 0$

Step 2

Divide each term in $8 x \geq 0$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 x \geq 0$ by $8$ .

$\frac{8 x}{8} \geq \frac{0}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} \geq \frac{0}{8}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{0}{8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $8$ .

$x \geq 0$

Step 3

Set the radicand in $\sqrt{8 x^{2}}$ greater than or equal to $0$ to find where the expression is defined.

$8 x^{2} \geq 0$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $8 x^{2} \geq 0$ by $8$ and simplify.

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Step 4.1.1

Divide each term in $8 x^{2} \geq 0$ by $8$ .

$\frac{8 x^{2}}{8} \geq \frac{0}{8}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $8$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{8 x^{2}}{8} \geq \frac{0}{8}$

Step 4.1.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} \geq \frac{0}{8}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $8$ .

$x^{2} \geq 0$

Step 4.2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 5

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 6