Solve for y square root of 3y+7=10

$\sqrt{3 y} + 7 = 10$

Step 1

Move all terms not containing $\sqrt{3 y}$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$\sqrt{3 y} = 10 - 7$

Subtract $7$ from $10$ .

$\sqrt{3 y} = 3$

Step 2

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

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

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(3 y)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 y)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$3 y = 3^{2}$

Simplify the right side.

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

$3 y = 9$

Step 4

Divide each term in $3 y = 9$ by $3$ and simplify.

Divide each term in $3 y = 9$ by $3$ .

$\frac{3 y}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{9}{3}$

Divide $y$ by $1$ .

$y = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$y = 3$