Simplify ( square root of 3- square root of 7)( square root of 3)+2 square root of 7

$(\sqrt{3} - \sqrt{7}) (\sqrt{3}) + 2 \sqrt{7}$

Step 1

Apply the distributive property.

$\sqrt{3} \sqrt{3} - \sqrt{7} \sqrt{3} + 2 \sqrt{7}$

Step 2

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} - \sqrt{7} \sqrt{3} + 2 \sqrt{7}$

Step 3

Multiply $- \sqrt{7} \sqrt{3}$ .

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} - \sqrt{3 \cdot 7} + 2 \sqrt{7}$

Multiply $3$ by $7$ .

$\sqrt{3 \cdot 3} - \sqrt{21} + 2 \sqrt{7}$

Step 4

Simplify each term.

Multiply $3$ by $3$ .

$\sqrt{9} - \sqrt{21} + 2 \sqrt{7}$

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

$\sqrt{3^{2}} - \sqrt{21} + 2 \sqrt{7}$

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

$3 - \sqrt{21} + 2 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 - \sqrt{21} + 2 \sqrt{7}$

Decimal Form:

$3.70892692 \dots$