Precalculus Examples

$\sqrt{y + 2} = 3$

Step 1

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

${\sqrt{y + 2}}^{2} = 3^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

${(y + 2)}^{1} = 3^{2}$

Step 2.2.1.2

Simplify.

$y + 2 = 3^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$y + 2 = 9$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$y = 9 - 2$

Step 3.2

Subtract $2$ from $9$ .

$y = 7$