Simplify square root of (3- square root of 15)^2- square root of (3+ square root of 15)^2

$\sqrt{{(3 - \sqrt{15})}^{2}} - \sqrt{{(3 + \sqrt{15})}^{2}}$

Step 1

Simplify each term.

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

$3 - \sqrt{15} - \sqrt{{(3 + \sqrt{15})}^{2}}$

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

$3 - \sqrt{15} - (3 + \sqrt{15})$

Apply the distributive property.

$3 - \sqrt{15} - 1 \cdot 3 - \sqrt{15}$

Multiply $- 1$ by $3$ .

$3 - \sqrt{15} - 3 - \sqrt{15}$

Step 2

Simplify by adding terms.

Subtract $3$ from $3$ .

$0 - \sqrt{15} - \sqrt{15}$

Subtract $\sqrt{15}$ from $0$ .

$- \sqrt{15} - \sqrt{15}$

Subtract $\sqrt{15}$ from $- \sqrt{15}$ .

$- 2 \sqrt{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{15}$

Decimal Form:

$- 7.74596669 \dots$