Simplify ( square root of x+1)^2-1

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

Step 1

Rewrite ${\sqrt{x + 1}}^{2}$ as $x + 1$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x + 1 - 1$

Step 2

Combine the opposite terms in $x + 1 - 1$ .

Subtract $1$ from $1$ .

$x + 0$

Add $x$ and $0$ .

$x$