Basic Math Examples

$a = \sqrt{b c + d}$

Step 1

Rewrite the equation as $\sqrt{b c + d} = a$ .

$\sqrt{b c + d} = a$

Step 2

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

${\sqrt{b c + d}}^{2} = a^{2}$

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 $\sqrt{b c + d}$ as ${(b c + d)}^{\frac{1}{2}}$ .

${({(b c + d)}^{\frac{1}{2}})}^{2} = a^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(b c + d)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(b c + d)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(b c + d)}^{\frac{1}{2} \cdot 2} = a^{2}$

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.

${(b c + d)}^{\frac{1}{2} \cdot 2} = a^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(b c + d)}^{1} = a^{2}$

Step 3.2.1.2

Simplify.

$b c + d = a^{2}$

Step 4

Solve for $b$ .

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Step 4.1

Subtract $d$ from both sides of the equation.

$b c = a^{2} - d$

Step 4.2

Divide each term in $b c = a^{2} - d$ by $c$ and simplify.

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Step 4.2.1

Divide each term in $b c = a^{2} - d$ by $c$ .

$\frac{b c}{c} = \frac{a^{2}}{c} + \frac{- d}{c}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $c$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{b c}{c} = \frac{a^{2}}{c} + \frac{- d}{c}$

Step 4.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{a^{2}}{c} + \frac{- d}{c}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$b = \frac{a^{2}}{c} - \frac{d}{c}$