Simplify the Radical Expression - square root of 72- square root of 200

$- \sqrt{72} - \sqrt{200}$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

$- \sqrt{36 (2)} - \sqrt{200}$

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

$- \sqrt{6^{2} \cdot 2} - \sqrt{200}$

Pull terms out from under the radical.

$- (| 6 | \sqrt{2}) - \sqrt{200}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$- (6 \sqrt{2}) - \sqrt{200}$

Multiply $6$ by $- 1$ .

$- 6 \sqrt{2} - \sqrt{200}$

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$- 6 \sqrt{2} - \sqrt{100 (2)}$

Rewrite $100$ as $10^{2}$ .

$- 6 \sqrt{2} - \sqrt{10^{2} \cdot 2}$

Pull terms out from under the radical.

$- 6 \sqrt{2} - (| 10 | \sqrt{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$- 6 \sqrt{2} - (10 \sqrt{2})$

Multiply $10$ by $- 1$ .

$- 6 \sqrt{2} - 10 \sqrt{2}$

Step 2

Subtract $10 \sqrt{2}$ from $- 6 \sqrt{2}$ .

$- 16 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 16 \sqrt{2}$

Decimal Form:

$- 22.62741699 \dots$