Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $3$ by $7$ .

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Combine using the product rule for radicals.

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

Step 1.5

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.

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Step 2.1

Multiply $3$ by $21$ .

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

Step 2.2

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

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Step 2.2.1

Factor $9$ out of $63$ .

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

Step 2.2.2

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

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

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

Step 2.3

Pull terms out from under the radical.

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

Step 2.4

Multiply $7$ by $21$ .

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

Step 2.5

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

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Step 2.5.1

Factor $49$ out of $147$ .

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

Step 2.5.2

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

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

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

Step 2.6

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:

$20.06160958 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$