Simplify square root of 5*-2 square root of 5

$\sqrt{5} \cdot - 2 \sqrt{5}$

Step 1

Multiply $\sqrt{5} (- 2 \sqrt{5})$ .

Raise $\sqrt{5}$ to the power of $1$ .

$- 2 ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$- 2 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$- 2 {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$- 2 {\sqrt{5}}^{2}$

Step 2

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$- 2 {(5^{\frac{1}{2}})}^{2}$

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

$- 2 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$- 2 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 2 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$- 2 \cdot 5^{1}$

Evaluate the exponent.

$- 2 \cdot 5$

Step 3

Multiply $- 2$ by $5$ .

$- 10$