Solve by Factoring square root of 3x+1-5=0

$\sqrt{3 x + 1} - 5 = 0$

Step 1

Add $5$ to both sides of the equation.

$\sqrt{3 x + 1} = 5$

Step 2

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

${\sqrt{3 x + 1}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

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

${({(3 x + 1)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

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

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

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

${(3 x + 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x + 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(3 x + 1)}^{1} = 5^{2}$

Simplify.

$3 x + 1 = 5^{2}$

Simplify the right side.

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

$3 x + 1 = 25$

Step 4

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$3 x = 25 - 1$

Subtract $1$ from $25$ .

$3 x = 24$

Divide each term in $3 x = 24$ by $3$ and simplify.

Divide each term in $3 x = 24$ by $3$ .

$\frac{3 x}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{24}{3}$

Divide $x$ by $1$ .

$x = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x = 8$