Pre-Algebra Examples

$\sqrt{r + 5} + 6 = 9$

Step 1

Move all terms not containing $\sqrt{r + 5}$ to the right side of the equation.

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Step 1.1

Subtract $6$ from both sides of the equation.

$\sqrt{r + 5} = 9 - 6$

Step 1.2

Subtract $6$ from $9$ .

$\sqrt{r + 5} = 3$

Step 2

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

${\sqrt{r + 5}}^{2} = 3^{2}$

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 $\sqrt{r + 5}$ as ${(r + 5)}^{\frac{1}{2}}$ .

${({(r + 5)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(r + 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(r + 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(r + 5)}^{\frac{1}{2} \cdot 2} = 3^{2}$

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.

${(r + 5)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(r + 5)}^{1} = 3^{2}$

Step 3.2.1.2

Simplify.

$r + 5 = 3^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $3$ to the power of $2$ .

$r + 5 = 9$

Step 4

Move all terms not containing $r$ to the right side of the equation.

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Step 4.1

Subtract $5$ from both sides of the equation.

$r = 9 - 5$

Step 4.2

Subtract $5$ from $9$ .

$r = 4$