Simplify (-1/2 square root of 2)(-6 square root of 18)

$(- \frac{1}{2} \sqrt{2}) (- 6 \sqrt{18})$

Step 1

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

$- \frac{\sqrt{2}}{2} (- 6 \sqrt{18})$

Step 2

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{\sqrt{2}}{2}$ into the numerator.

$\frac{- \sqrt{2}}{2} (- 6 \sqrt{18})$

Factor $2$ out of $- 6 \sqrt{18}$ .

$\frac{- \sqrt{2}}{2} (2 (- 3 \sqrt{18}))$

Cancel the common factor.

$\frac{- \sqrt{2}}{2} (2 (- 3 \sqrt{18}))$

Rewrite the expression.

$- \sqrt{2} (- 3 \sqrt{18})$

Step 3

Multiply $- 3$ by $- 1$ .

$3 \sqrt{2} \sqrt{18}$

Step 4

Combine using the product rule for radicals.

$3 \sqrt{18 \cdot 2}$

Step 5

Write the expression using exponents.

Multiply $18$ by $2$ .

$3 \sqrt{36}$

Rewrite $36$ as $6^{2}$ .

$3 \sqrt{6^{2}}$

Multiply.

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

$3 \cdot 6$

Multiply $3$ by $6$ .

$18$