Algebra Examples Radical Expressions and Equations

Find the Square Root End Point

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

Step 1

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

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Step 1.1

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

$x \geq 0$

Step 1.2

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 $\sqrt{x}$ .

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Step 2.1

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

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

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

Step 2.2.3

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

$f (0) = 0$

Step 2.2.4

The final answer is $0$ .

$y = 0$

Step 3

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

$(0, 0)$

Step 4

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Find the Square Root End Point

Radical Expressions and Equations

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