Simplify square root of 3*(- square root of 3)

$\sqrt{3} \cdot (- \sqrt{3})$

Step 1

Multiply $\sqrt{3} (- \sqrt{3})$ .

Raise $\sqrt{3}$ to the power of $1$ .

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

Raise $\sqrt{3}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

$- {\sqrt{3}}^{2}$

Step 2

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

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

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

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

$- 3^{\frac{1}{2} \cdot 2}$

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

$- 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 3^{\frac{2}{2}}$

Rewrite the expression.

$- 3^{1}$

Evaluate the exponent.

$- 1 \cdot 3$

Step 3

Multiply $- 1$ by $3$ .

$- 3$