Algebra Examples

$\sqrt{y^{15}}$

Step 1

Set the radicand in $\sqrt{y^{15}}$ greater than or equal to $0$ to find where the expression is defined.

$y^{15} \geq 0$

Step 2

Solve for $y$ .

Tap for more steps...

Step 2.1

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

$\sqrt[15]{y^{15}} \geq \sqrt[15]{0}$

Step 2.2

Simplify the equation.

Tap for more steps...

Step 2.2.1

Simplify the left side.

Tap for more steps...

Step 2.2.1.1

Pull terms out from under the radical.

$y \geq \sqrt[15]{0}$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Simplify $\sqrt[15]{0}$ .

Tap for more steps...

Step 2.2.2.1.1

Rewrite $0$ as $0^{15}$ .

$y \geq \sqrt[15]{0^{15}}$

Step 2.2.2.1.2

Pull terms out from under the radical.

$y \geq 0$

Step 3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Step 4