Linear Algebra Examples

$\sqrt{25 x^{6}}$

Step 1

Set the radicand in $\sqrt{25 x^{6}}$ greater than or equal to $0$ to find where the expression is defined.

$25 x^{6} \geq 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Divide each term in $25 x^{6} \geq 0$ by $25$ and simplify.

Tap for more steps...

Step 2.1.1

Divide each term in $25 x^{6} \geq 0$ by $25$ .

$\frac{25 x^{6}}{25} \geq \frac{0}{25}$

Step 2.1.2

Simplify the left side.

Tap for more steps...

Step 2.1.2.1

Cancel the common factor of $25$ .

Tap for more steps...

Step 2.1.2.1.1

Cancel the common factor.

$\frac{25 x^{6}}{25} \geq \frac{0}{25}$

Step 2.1.2.1.2

Divide $x^{6}$ by $1$ .

$x^{6} \geq \frac{0}{25}$

Step 2.1.3

Simplify the right side.

Tap for more steps...

Step 2.1.3.1

Divide $0$ by $25$ .

$x^{6} \geq 0$

Step 2.2

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

All real numbers

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4