Find the Roots (Zeros) f(x) = square root of x-1

$f (x) = \sqrt{x - 1}$

Step 1

Set $\sqrt{x - 1}$ equal to $0$ .

$\sqrt{x - 1} = 0$

Step 2

Solve for $x$ .

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

${\sqrt{x - 1}}^{2} = 0^{2}$

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 1 = 0^{2}$

Simplify the right side.

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 3