Solve the Rational Equation for x square root of x-3-2=0

$\sqrt{x - 3} - 2 = 0$

Add $2$ to both sides of the equation.

$\sqrt{x - 3} = 2$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 3 = 2^{2}$

Simplify the right side.

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

$x - 3 = 4$

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

Add $3$ to both sides of the equation.

$x = 4 + 3$

Add $4$ and $3$ .

$x = 7$