Solve by Factoring square root of x-1=3

$\sqrt{x - 1} = 3$

Step 1

Subtract $3$ from both sides of the equation.

$\sqrt{x - 1} - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$\sqrt{x - 1} = 3$

Step 3

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

${\sqrt{x - 1}}^{2} = 3^{2}$

Step 4

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 1 = 3^{2}$

Simplify the right side.

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

$x - 1 = 9$

Step 5

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

Add $1$ to both sides of the equation.

$x = 9 + 1$

Add $9$ and $1$ .

$x = 10$