Find the Square Root End Point square root of x^21

$\sqrt{x^{21}}$

Step 1

Find the domain for $\sqrt{x^{21}}$ .

Set the radicand in $\sqrt{x^{21}}$ greater than or equal to $0$ to find where the expression is defined.

$x^{21} \geq 0$

Solve for $x$ .

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

$\sqrt[21]{x^{21}} \geq \sqrt[21]{0}$

Simplify the equation.

Simplify the left side.

Pull terms out from under the radical.

$x \geq \sqrt[21]{0}$

Simplify the right side.

Simplify $\sqrt[21]{0}$ .

Rewrite $0$ as $0^{21}$ .

$x \geq \sqrt[21]{0^{21}}$

Pull terms out from under the radical.

$x \geq 0$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 2

To find the square root end point, substitute the $x$ value $0$ , which is the terminal value in the domain, into $\sqrt{x^{21}}$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = \sqrt{{(0)}^{21}}$

Simplify the result.

Raising $0$ to any positive power yields $0$ .

$f (0) = \sqrt{0}$

Rewrite $0$ as $0^{2}$ .

$f (0) = \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$f (0) = 0$

The final answer is $0$ .

$y = 0$

Step 3

The square root end point is $(0, 0)$ .

$(0, 0)$

Step 4