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

$\sqrt{x - 4} = 0$

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

${\sqrt{x - 4}}^{2} = 0^{2}$

Simplify each side of the equation.

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

${({(x - 4)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

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

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

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

${(x - 4)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 4)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(x - 4)}^{1} = 0^{2}$

Simplify.

$x - 4 = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$