Solve by Factoring square root of 3x-1=7

$\sqrt{3 x - 1} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$\sqrt{3 x - 1} - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$\sqrt{3 x - 1} = 7$

Step 3

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

${\sqrt{3 x - 1}}^{2} = 7^{2}$

Step 4

Simplify each side of the equation.

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

${({(3 x - 1)}^{\frac{1}{2}})}^{2} = 7^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 1)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(3 x - 1)}^{1} = 7^{2}$

Simplify.

$3 x - 1 = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$3 x - 1 = 49$

Step 5

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$3 x = 49 + 1$

Add $49$ and $1$ .

$3 x = 50$

Divide each term in $3 x = 50$ by $3$ and simplify.

Divide each term in $3 x = 50$ by $3$ .

$\frac{3 x}{3} = \frac{50}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{50}{3}$

Divide $x$ by $1$ .

$x = \frac{50}{3}$