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

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

Step 1

Subtract $4$ from both sides of the equation.

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

Step 2

Add $4$ to both sides of the equation.

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

Step 3

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

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

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 4}$ as ${(5 x - 4)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(5 x - 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x - 4)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$5 x - 4 = 16$

Step 5

Solve for $x$ .

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

Add $4$ to both sides of the equation.

$5 x = 16 + 4$

Add $16$ and $4$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

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

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