Simplify ( square root of 3+ square root of 7)( square root of 3* square root of 7)

$(\sqrt{3} + \sqrt{7}) (\sqrt{3} \cdot \sqrt{7})$

Step 1

Simplify terms.

Combine using the product rule for radicals.

$(\sqrt{3} + \sqrt{7}) \sqrt{3 \cdot 7}$

Multiply $3$ by $7$ .

$(\sqrt{3} + \sqrt{7}) \sqrt{21}$

Apply the distributive property.

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

Combine using the product rule for radicals.

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

Combine using the product rule for radicals.

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

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

Step 2

Simplify each term.

Multiply $3$ by $21$ .

$\sqrt{63} + \sqrt{7 \cdot 21}$

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$\sqrt{9 (7)} + \sqrt{7 \cdot 21}$

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

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

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

Pull terms out from under the radical.

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

Multiply $7$ by $21$ .

$3 \sqrt{7} + \sqrt{147}$

Rewrite $147$ as $7^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$3 \sqrt{7} + \sqrt{49 (3)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$20.06160958 \dots$

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