Trigonometry Examples

${(\frac{2 h}{32})}^{\frac{1}{2}}$

Step 1

Convert expressions with fractional exponents to radicals.

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Step 1.1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{{(\frac{2 h}{32})}^{1}}$

Step 1.2

Anything raised to $1$ is the base itself.

$\sqrt{\frac{2 h}{32}}$

Step 2

Set the radicand in $\sqrt{\frac{2 h}{32}}$ greater than or equal to $0$ to find where the expression is defined.

$\frac{2 h}{32} \geq 0$

Step 3

Solve for $h$ .

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Step 3.1

Cancel the common factor of $2$ and $32$ .

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Step 3.1.1

Factor $2$ out of $2 h$ .

$\frac{2 (h)}{32} \geq 0$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $32$ .

$\frac{2 h}{2 \cdot 16} \geq 0$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 h}{2 \cdot 16} \geq 0$

Step 3.1.2.3

Rewrite the expression.

$\frac{h}{16} \geq 0$

Step 3.2

Multiply both sides by $16$ .

$\frac{h}{16} \cdot 16 \geq 0 \cdot 16$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $16$ .

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Step 3.3.1.1.1

Cancel the common factor.

$\frac{h}{16} \cdot 16 \geq 0 \cdot 16$

Step 3.3.1.1.2

Rewrite the expression.

$h \geq 0 \cdot 16$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $0$ by $16$ .

$h \geq 0$

Step 4

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${h | h \geq 0}$

Step 5