Solve the Rational Equation for x 3- square root of x-4=0

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

Step 1

Subtract $3$ from both sides of the equation.

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $- {(x - 4)}^{\frac{1}{2}}$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply ${({(x - 4)}^{\frac{1}{2}})}^{2}$ by $1$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 3$ to the power of $2$ .

$x - 4 = 9$

Step 4

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

Add $4$ to both sides of the equation.

$x = 9 + 4$

Add $9$ and $4$ .

$x = 13$