Algebra Examples

$3.2 = 2 π \sqrt{\frac{l}{32}}$

Rewrite the equation as $2 π \sqrt{\frac{l}{32}} = 3.2$ .

$2 π \sqrt{\frac{l}{32}} = 3.2$

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

${(2 π \sqrt{\frac{l}{32}})}^{2} = {3.2}^{2}$

Simplify each side of the equation.

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{32}}$ as ${(\frac{l}{32})}^{\frac{1}{2}}$ .

${(2 π {(\frac{l}{32})}^{\frac{1}{2}})}^{2} = {3.2}^{2}$

Simplify the left side.

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Simplify ${(2 π {(\frac{l}{32})}^{\frac{1}{2}})}^{2}$ .

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Apply the product rule to $\frac{l}{32}$ .

${(2 π \frac{l^{\frac{1}{2}}}{32^{\frac{1}{2}}})}^{2} = {3.2}^{2}$

Multiply $2 π \frac{l^{\frac{1}{2}}}{32^{\frac{1}{2}}}$ .

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Combine $\frac{l^{\frac{1}{2}}}{32^{\frac{1}{2}}}$ and $2$ .

${(\frac{l^{\frac{1}{2}} \cdot 2}{32^{\frac{1}{2}}} π)}^{2} = {3.2}^{2}$

Combine $\frac{l^{\frac{1}{2}} \cdot 2}{32^{\frac{1}{2}}}$ and $π$ .

${(\frac{l^{\frac{1}{2}} \cdot 2 π}{32^{\frac{1}{2}}})}^{2} = {3.2}^{2}$

Move $2$ to the left of $l^{\frac{1}{2}}$ .

${(\frac{2 \cdot l^{\frac{1}{2}} π}{32^{\frac{1}{2}}})}^{2} = {3.2}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $\frac{2 l^{\frac{1}{2}} π}{32^{\frac{1}{2}}}$ .

$\frac{{(2 l^{\frac{1}{2}} π)}^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Apply the product rule to $2 l^{\frac{1}{2}} π$ .

$\frac{{(2 l^{\frac{1}{2}})}^{2} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Apply the product rule to $2 l^{\frac{1}{2}}$ .

$\frac{2^{2} {(l^{\frac{1}{2}})}^{2} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Simplify the numerator.

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

$\frac{4 {(l^{\frac{1}{2}})}^{2} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Multiply the exponents in ${(l^{\frac{1}{2}})}^{2}$ .

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

$\frac{4 l^{\frac{1}{2} \cdot 2} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4 l^{\frac{1}{2} \cdot 2} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Rewrite the expression.

$\frac{4 l^{1} π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Simplify.

$\frac{4 l π^{2}}{{(32^{\frac{1}{2}})}^{2}} = {3.2}^{2}$

Simplify the denominator.

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Multiply the exponents in ${(32^{\frac{1}{2}})}^{2}$ .

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

$\frac{4 l π^{2}}{32^{\frac{1}{2} \cdot 2}} = {3.2}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4 l π^{2}}{32^{\frac{1}{2} \cdot 2}} = {3.2}^{2}$

Rewrite the expression.

$\frac{4 l π^{2}}{32^{1}} = {3.2}^{2}$

Evaluate the exponent.

$\frac{4 l π^{2}}{32} = {3.2}^{2}$

Cancel the common factor of $4$ and $32$ .

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Factor $4$ out of $4 l π^{2}$ .

$\frac{4 (l π^{2})}{32} = {3.2}^{2}$

Cancel the common factors.

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Factor $4$ out of $32$ .

$\frac{4 (l π^{2})}{4 \cdot 8} = {3.2}^{2}$

Cancel the common factor.

$\frac{4 (l π^{2})}{4 \cdot 8} = {3.2}^{2}$

Rewrite the expression.

$\frac{l π^{2}}{8} = {3.2}^{2}$

Simplify the right side.

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Raise $3.2$ to the power of $2$ .

$\frac{l π^{2}}{8} = 10.24$

Solve for $l$ .

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Multiply both sides of the equation by $\frac{8}{π^{2}}$ .

$\frac{8}{π^{2}} \cdot \frac{l π^{2}}{8} = \frac{8}{π^{2}} \cdot 10.24$

Simplify both sides of the equation.

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Simplify the left side.

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Simplify $\frac{8}{π^{2}} \cdot \frac{l π^{2}}{8}$ .

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Combine.

$\frac{8 (l π^{2})}{π^{2} \cdot 8} = \frac{8}{π^{2}} \cdot 10.24$

Cancel the common factor of $8$ .

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Cancel the common factor.

$\frac{8 (l π^{2})}{π^{2} \cdot 8} = \frac{8}{π^{2}} \cdot 10.24$

Rewrite the expression.

$\frac{l π^{2}}{π^{2}} = \frac{8}{π^{2}} \cdot 10.24$

Cancel the common factor of $π^{2}$ .

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Cancel the common factor.

$\frac{l π^{2}}{π^{2}} = \frac{8}{π^{2}} \cdot 10.24$

Divide $l$ by $1$ .

$l = \frac{8}{π^{2}} \cdot 10.24$

Simplify the right side.

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Simplify $\frac{8}{π^{2}} \cdot 10.24$ .

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Multiply $\frac{8}{π^{2}} \cdot 10.24$ .

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Combine $\frac{8}{π^{2}}$ and $10.24$ .

$l = \frac{8 \cdot 10.24}{π^{2}}$

Multiply $8$ by $10.24$ .

$l = \frac{81.92}{π^{2}}$

Replace $π$ with an approximation.

$l = \frac{81.92}{{3.14159265}^{2}}$

Raise $3.14159265$ to the power of $2$ .

$l = \frac{81.92}{9.8696044}$

Divide $81.92$ by $9.8696044$ .

$l = 8.30023136$