Basic Math Examples

T = \sqrt{\frac{2 d}{g}}

$T = \sqrt{\frac{2 d}{g}}$

Step 1

Rewrite the equation as

\sqrt{\frac{2 d}{g}} = T

$\sqrt{\frac{2 d}{g}} = T$ .

\sqrt{\frac{2 d}{g}} = T

$\sqrt{\frac{2 d}{g}} = T$

Step 2

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

{\sqrt{\frac{2 d}{g}}}^{2} = T^{2}

${\sqrt{\frac{2 d}{g}}}^{2} = T^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{\frac{2 d}{g}}

$\sqrt{\frac{2 d}{g}}$ as

{(\frac{2 d}{g})}^{\frac{1}{2}}

${(\frac{2 d}{g})}^{\frac{1}{2}}$ .

{({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2} = T^{2}

${({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2} = T^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify

{({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2}

${({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in

{({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2}

${({(\frac{2 d}{g})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

{(\frac{2 d}{g})}^{\frac{1}{2} \cdot 2} = T^{2}

${(\frac{2 d}{g})}^{\frac{1}{2} \cdot 2} = T^{2}$

Step 3.2.1.1.2

Cancel the common factor of

2

$2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{2 d}{g})}^{\frac{1}{2} \cdot 2} = T^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{2 d}{g})}^{1} = T^{2}$

Step 3.2.1.2

Simplify.

$\frac{2 d}{g} = T^{2}$

Step 4

Solve for

$g$ .

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Step 4.1

Find the LCD of the terms in the equation.

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Step 4.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$g, 1$

Step 4.1.2

The LCM of one and any expression is the expression.

$g$

Step 4.2

Multiply each term in

$\frac{2 d}{g} = T^{2}$ by

$g$ to eliminate the fractions.

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Step 4.2.1

Multiply each term in

$\frac{2 d}{g} = T^{2}$ by

$g$ .

$\frac{2 d}{g} g = T^{2} g$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

$g$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 d}{g} g = T^{2} g$

Step 4.2.2.1.2

Rewrite the expression.

$2 d = T^{2} g$

Step 4.3

Solve the equation.

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Step 4.3.1

Rewrite the equation as

$T^{2} g = 2 d$ .

$T^{2} g = 2 d$

Step 4.3.2

Divide each term in

$T^{2} g = 2 d$ by

$T^{2}$ and simplify.

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Step 4.3.2.1

Divide each term in

$T^{2} g = 2 d$ by

$T^{2}$ .

$\frac{T^{2} g}{T^{2}} = \frac{2 d}{T^{2}}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

Cancel the common factor of

$T^{2}$ .

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{T^{2} g}{T^{2}} = \frac{2 d}{T^{2}}$

Step 4.3.2.2.1.2

Divide

$g$ by

$1$ .

$g = \frac{2 d}{T^{2}}$