Algebra Examples

$T = 2 (3.14) \sqrt{\frac{L}{32}}$

Step 1

Rewrite the equation as $2 (3.14) \sqrt{\frac{L}{32}} = T$ .

$2 (3.14) \sqrt{\frac{L}{32}} = T$

Step 2

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

${(2 (3.14) \sqrt{\frac{L}{32}})}^{2} = T^{2}$

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 $\sqrt{\frac{L}{32}}$ as ${(\frac{L}{32})}^{\frac{1}{2}}$ .

${(2 (3.14) {(\frac{L}{32})}^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(2 (3.14) {(\frac{L}{32})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

Multiply $2$ by $3.14$ .

${(6.28 {(\frac{L}{32})}^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2.1.1.2

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

${(6.28 \frac{L^{\frac{1}{2}}}{32^{\frac{1}{2}}})}^{2} = T^{2}$

Step 3.2.1.2

Combine $6.28$ and $\frac{L^{\frac{1}{2}}}{32^{\frac{1}{2}}}$ .

${(\frac{6.28 L^{\frac{1}{2}}}{32^{\frac{1}{2}}})}^{2} = T^{2}$

Step 3.2.1.3

Factor $6.28$ out of $6.28 L^{\frac{1}{2}}$ .

${(\frac{6.28 (L^{\frac{1}{2}})}{32^{\frac{1}{2}}})}^{2} = T^{2}$

Step 3.2.1.4

Multiply by $1$ .

${(\frac{6.28 (L^{\frac{1}{2}})}{32^{\frac{1}{2}} \cdot 1})}^{2} = T^{2}$

Step 3.2.1.5

Separate fractions.

${(\frac{6.28}{32^{\frac{1}{2}}} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = T^{2}$

Step 3.2.1.6

Divide $1$ by $2$ .

${(\frac{6.28}{32^{0.5}} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = T^{2}$

Step 3.2.1.7

Raise $32$ to the power of $0.5$ .

${(\frac{6.28}{5.65685424} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = T^{2}$

Step 3.2.1.8

Divide $6.28$ by $5.65685424$ .

${(1.11015764 \frac{L^{\frac{1}{2}}}{1})}^{2} = T^{2}$

Step 3.2.1.9

Divide $L^{\frac{1}{2}}$ by $1$ .

${(1.11015764 L^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2.1.10

Apply the product rule to $1.11015764 L^{\frac{1}{2}}$ .

${1.11015764}^{2} {(L^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2.1.11

Raise $1.11015764$ to the power of $2$ .

$1.23245 {(L^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2.1.12

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

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Step 3.2.1.12.1

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

$1.23245 L^{\frac{1}{2} \cdot 2} = T^{2}$

Step 3.2.1.12.2

Cancel the common factor of $2$ .

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Step 3.2.1.12.2.1

Cancel the common factor.

$1.23245 L^{\frac{1}{2} \cdot 2} = T^{2}$

Step 3.2.1.12.2.2

Rewrite the expression.

$1.23245 L^{1} = T^{2}$

Step 3.2.1.13

Simplify.

$1.23245 L = T^{2}$

Step 4

Divide each term in $1.23245 L = T^{2}$ by $1.23245$ and simplify.

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Step 4.1

Divide each term in $1.23245 L = T^{2}$ by $1.23245$ .

$\frac{1.23245 L}{1.23245} = \frac{T^{2}}{1.23245}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1.23245$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1.23245 L}{1.23245} = \frac{T^{2}}{1.23245}$

Step 4.2.1.2

Divide $L$ by $1$ .

$L = \frac{T^{2}}{1.23245}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply by $1$ .

$L = \frac{1 T^{2}}{1.23245}$

Step 4.3.2

Factor $1.23245$ out of $1.23245$ .

$L = \frac{1 T^{2}}{1.23245 (1)}$

Step 4.3.3

Separate fractions.

$L = \frac{1}{1.23245} \cdot \frac{T^{2}}{1}$

Step 4.3.4

Divide $1$ by $1.23245$ .

$L = 0.81139194 \frac{T^{2}}{1}$

Step 4.3.5

Divide $T^{2}$ by $1$ .

$L = 0.81139194 T^{2}$