Trigonometry Examples

$32 = \sqrt{2 \cdot (176 x)}$

Step 1

Rewrite the equation as $\sqrt{2 \cdot (176 x)} = 32$ .

$\sqrt{2 \cdot (176 x)} = 32$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 \cdot (176 x)}}^{2} = 32^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 \cdot (176 x)}$ as ${(2 \cdot (176 x))}^{\frac{1}{2}}$ .

${({(2 \cdot (176 x))}^{\frac{1}{2}})}^{2} = 32^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(2 \cdot (176 x))}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(2 \cdot (176 x))}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 \cdot (176 x))}^{\frac{1}{2} \cdot 2} = 32^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(2 \cdot (176 x))}^{\frac{1}{2} \cdot 2} = 32^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 \cdot (176 x))}^{1} = 32^{2}$

Step 3.2.1.2

Multiply $176$ by $2$ .

${(352 x)}^{1} = 32^{2}$

Step 3.2.1.3

Simplify.

$352 x = 32^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $32$ to the power of $2$ .

$352 x = 1024$

Step 4

Divide each term in $352 x = 1024$ by $352$ and simplify.

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Step 4.1

Divide each term in $352 x = 1024$ by $352$ .

$\frac{352 x}{352} = \frac{1024}{352}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $352$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{352 x}{352} = \frac{1024}{352}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{1024}{352}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $1024$ and $352$ .

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Step 4.3.1.1

Factor $32$ out of $1024$ .

$x = \frac{32 (32)}{352}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $32$ out of $352$ .

$x = \frac{32 \cdot 32}{32 \cdot 11}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{32 \cdot 32}{32 \cdot 11}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{32}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{32}{11}$

Decimal Form:

$x = 2.\overline{90}$

Mixed Number Form:

$x = 2 \frac{10}{11}$