Solve by Factoring square root of 3x-5-4=0

$\sqrt{3 x - 5} - 4 = 0$

Step 1

Add $4$ to both sides of the equation.

$\sqrt{3 x - 5} = 4$

Step 2

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

${\sqrt{3 x - 5}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 5}$ as ${(3 x - 5)}^{\frac{1}{2}}$ .

${({(3 x - 5)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(3 x - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(3 x - 5)}^{1} = 4^{2}$

Simplify.

$3 x - 5 = 4^{2}$

Simplify the right side.

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

$3 x - 5 = 16$

Step 4

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$3 x = 16 + 5$

Add $16$ and $5$ .

$3 x = 21$

Divide each term in $3 x = 21$ by $3$ and simplify.

Divide each term in $3 x = 21$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3}$

Divide $x$ by $1$ .

$x = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x = 7$