Solve by Factoring 3( square root of y+4)=15

$3 (\sqrt{y + 4}) = 15$

Step 1

Subtract $15$ from both sides of the equation.

$3 (\sqrt{y + 4}) - 15 = 0$

Step 2

Multiply $3$ by $\sqrt{y + 4}$ .

$3 \sqrt{y + 4} - 15 = 0$

Step 3

Factor $3$ out of $3 \sqrt{y + 4} - 15$ .

Factor $3$ out of $3 \sqrt{y + 4}$ .

$3 (\sqrt{y + 4}) - 15 = 0$

Factor $3$ out of $- 15$ .

$3 \sqrt{y + 4} + 3 \cdot - 5 = 0$

Factor $3$ out of $3 \sqrt{y + 4} + 3 \cdot - 5$ .

$3 (\sqrt{y + 4} - 5) = 0$

Step 4

Divide each term in $3 (\sqrt{y + 4} - 5) = 0$ by $3$ and simplify.

Divide each term in $3 (\sqrt{y + 4} - 5) = 0$ by $3$ .

$\frac{3 (\sqrt{y + 4} - 5)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (\sqrt{y + 4} - 5)}{3} = \frac{0}{3}$

Divide $\sqrt{y + 4} - 5$ by $1$ .

$\sqrt{y + 4} - 5 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$\sqrt{y + 4} - 5 = 0$

Step 5

Add $5$ to both sides of the equation.

$\sqrt{y + 4} = 5$

Step 6

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

${\sqrt{y + 4}}^{2} = 5^{2}$

Step 7

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y + 4}$ as ${(y + 4)}^{\frac{1}{2}}$ .

${({(y + 4)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(y + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(y + 4)}^{\frac{1}{2}})}^{2}$ .

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

${(y + 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(y + 4)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(y + 4)}^{1} = 5^{2}$

Simplify.

$y + 4 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$y + 4 = 25$

Step 8

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

Subtract $4$ from both sides of the equation.

$y = 25 - 4$

Subtract $4$ from $25$ .

$y = 21$

Solve by Factoring 3( square root of y+4)=15

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