Simplify 1/2 square root of 98-6 square root of 72

$\frac{1}{2} \sqrt{98} - 6 \sqrt{72}$

Simplify each term.

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\frac{1}{2} \cdot \sqrt{49 (2)} - 6 \sqrt{72}$

Rewrite $49$ as $7^{2}$ .

$\frac{1}{2} \cdot \sqrt{7^{2} \cdot 2} - 6 \sqrt{72}$

Pull terms out from under the radical.

$\frac{1}{2} \cdot (7 \sqrt{2}) - 6 \sqrt{72}$

Multiply $\frac{1}{2} (7 \sqrt{2})$ .

Combine $7$ and $\frac{1}{2}$ .

$\frac{7}{2} \sqrt{2} - 6 \sqrt{72}$

Combine $\frac{7}{2}$ and $\sqrt{2}$ .

$\frac{7 \sqrt{2}}{2} - 6 \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\frac{7 \sqrt{2}}{2} - 6 \sqrt{36 (2)}$

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

$\frac{7 \sqrt{2}}{2} - 6 \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$\frac{7 \sqrt{2}}{2} - 6 (6 \sqrt{2})$

Multiply $6$ by $- 6$ .

$\frac{7 \sqrt{2}}{2} - 36 \sqrt{2}$

To write $- 36 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 \sqrt{2}}{2} - 36 \sqrt{2} \cdot \frac{2}{2}$

Combine fractions.

Combine $- 36 \sqrt{2}$ and $\frac{2}{2}$ .

$\frac{7 \sqrt{2}}{2} + \frac{- 36 \sqrt{2} \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{7 \sqrt{2} - 36 \sqrt{2} \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $- 36$ .

$\frac{7 \sqrt{2} - 72 \sqrt{2}}{2}$

Subtract $72 \sqrt{2}$ from $7 \sqrt{2}$ .

$\frac{- 65 \sqrt{2}}{2}$

Move the negative in front of the fraction.

$- \frac{65 \sqrt{2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{65 \sqrt{2}}{2}$

Decimal Form:

$- 45.96194077 \dots$