Evaluate ( square root of x-1)^2

${(\sqrt{x - 1})}^{2}$

Step 1

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

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

Step 2

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

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

Step 3

Combine $\frac{1}{2}$ and $2$ .

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(x - 1)}^{1}$

Step 5

Simplify.

$x - 1$