Solve for p 2+ square root of 3p+7=6

$2 + \sqrt{3 p + 7} = 6$

Move all terms not containing $\sqrt{3 p + 7}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{3 p + 7} = 6 - 2$

Subtract $2$ from $6$ .

$\sqrt{3 p + 7} = 4$

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

${\sqrt{3 p + 7}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 p + 7}$ as ${(3 p + 7)}^{\frac{1}{2}}$ .

${({(3 p + 7)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(3 p + 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 p + 7)}^{\frac{1}{2}})}^{2}$ .

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

${(3 p + 7)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 p + 7)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(3 p + 7)}^{1} = 4^{2}$

Simplify.

$3 p + 7 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$3 p + 7 = 16$

Solve for $p$ .

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

Subtract $7$ from both sides of the equation.

$3 p = 16 - 7$

Subtract $7$ from $16$ .

$3 p = 9$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

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

Simplify the right side.

Divide $9$ by $3$ .

$p = 3$