Solve for p 4 square root of 3p+1=16

$4 \sqrt{3 p + 1} = 16$

Step 1

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

${(4 \sqrt{3 p + 1})}^{2} = 16^{2}$

Step 2

Simplify each side of the equation.

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

${(4 {(3 p + 1)}^{\frac{1}{2}})}^{2} = 16^{2}$

Simplify the left side.

Simplify ${(4 {(3 p + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 {(3 p + 1)}^{\frac{1}{2}}$ .

$4^{2} {({(3 p + 1)}^{\frac{1}{2}})}^{2} = 16^{2}$

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

$16 {({(3 p + 1)}^{\frac{1}{2}})}^{2} = 16^{2}$

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

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

$16 {(3 p + 1)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(3 p + 1)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Rewrite the expression.

$16 {(3 p + 1)}^{1} = 16^{2}$

Simplify.

$16 (3 p + 1) = 16^{2}$

Apply the distributive property.

$16 (3 p) + 16 \cdot 1 = 16^{2}$

Multiply.

Multiply $3$ by $16$ .

$48 p + 16 \cdot 1 = 16^{2}$

Multiply $16$ by $1$ .

$48 p + 16 = 16^{2}$

Simplify the right side.

Raise $16$ to the power of $2$ .

$48 p + 16 = 256$

Step 3

Solve for $p$ .

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

Subtract $16$ from both sides of the equation.

$48 p = 256 - 16$

Subtract $16$ from $256$ .

$48 p = 240$

Divide each term in $48 p = 240$ by $48$ and simplify.

Divide each term in $48 p = 240$ by $48$ .

$\frac{48 p}{48} = \frac{240}{48}$

Simplify the left side.

Cancel the common factor of $48$ .

Cancel the common factor.

$\frac{48 p}{48} = \frac{240}{48}$

Divide $p$ by $1$ .

$p = \frac{240}{48}$

Simplify the right side.

Divide $240$ by $48$ .

$p = 5$

Solve for p 4 square root of 3p+1=16

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