Simplify 1/2 square root of 18-6 square root of 32

$\frac{1}{2} \sqrt{18} - 6 \sqrt{32}$

Step 1

Simplify each term.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{1}{2} \cdot \sqrt{9 (2)} - 6 \sqrt{32}$

Rewrite $9$ as $3^{2}$ .

$\frac{1}{2} \cdot \sqrt{3^{2} \cdot 2} - 6 \sqrt{32}$

Pull terms out from under the radical.

$\frac{1}{2} \cdot (3 \sqrt{2}) - 6 \sqrt{32}$

Multiply $\frac{1}{2} (3 \sqrt{2})$ .

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} \sqrt{2} - 6 \sqrt{32}$

Combine $\frac{3}{2}$ and $\sqrt{2}$ .

$\frac{3 \sqrt{2}}{2} - 6 \sqrt{32}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\frac{3 \sqrt{2}}{2} - 6 \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$\frac{3 \sqrt{2}}{2} - 6 \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$\frac{3 \sqrt{2}}{2} - 6 (4 \sqrt{2})$

Multiply $4$ by $- 6$ .

$\frac{3 \sqrt{2}}{2} - 24 \sqrt{2}$

Step 2

To write $- 24 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 \sqrt{2}}{2} - 24 \sqrt{2} \cdot \frac{2}{2}$

Step 3

Combine fractions.

Combine $- 24 \sqrt{2}$ and $\frac{2}{2}$ .

$\frac{3 \sqrt{2}}{2} + \frac{- 24 \sqrt{2} \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{3 \sqrt{2} - 24 \sqrt{2} \cdot 2}{2}$

Step 4

Simplify the numerator.

Multiply $2$ by $- 24$ .

$\frac{3 \sqrt{2} - 48 \sqrt{2}}{2}$

Subtract $48 \sqrt{2}$ from $3 \sqrt{2}$ .

$\frac{- 45 \sqrt{2}}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{45 \sqrt{2}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{45 \sqrt{2}}{2}$

Decimal Form:

$- 31.81980515 \dots$

Simplify 1/2 square root of 18-6 square root of 32

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