Evaluate square root of (-1)^2+( square root of 3)^2

$\sqrt{{(- 1)}^{2} + {(\sqrt{3})}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{1 + {(\sqrt{3})}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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

$\sqrt{1 + {(3^{\frac{1}{2}})}^{2}}$

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

$\sqrt{1 + 3^{\frac{1}{2} \cdot 2}}$

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

$\sqrt{1 + 3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\sqrt{1 + 3^{\frac{2}{2}}}$

Rewrite the expression.

$\sqrt{1 + 3^{1}}$

Evaluate the exponent.

$\sqrt{1 + 3}$

Simplify the expression.

Add $1$ and $3$ .

$\sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$2$