Basic Math Examples

$3 \sqrt{7} (\sqrt{14} + 4 \sqrt{56})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $56$ as $2^{2} \cdot 14$ .

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Step 1.1.1

Factor $4$ out of $56$ .

$3 \sqrt{7} (\sqrt{14} + 4 \sqrt{4 (14)})$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{7} (\sqrt{14} + 4 \sqrt{2^{2} \cdot 14})$

$3 \sqrt{7} (\sqrt{14} + 4 \sqrt{2^{2} \cdot 14})$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{7} (\sqrt{14} + 4 (2 \sqrt{14}))$

Step 1.3

Multiply $2$ by $4$ .

$3 \sqrt{7} (\sqrt{14} + 8 \sqrt{14})$

$3 \sqrt{7} (\sqrt{14} + 8 \sqrt{14})$

Step 2

Add $\sqrt{14}$ and $8 \sqrt{14}$ .

$3 \sqrt{7} (9 \sqrt{14})$

Step 3

Multiply $3 \sqrt{7} (9 \sqrt{14})$ .

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Step 3.1

Multiply $9$ by $3$ .

$27 \sqrt{7} \sqrt{14}$

Step 3.2

Combine using the product rule for radicals.

$27 \sqrt{14 \cdot 7}$

Step 3.3

Multiply $14$ by $7$ .

$27 \sqrt{98}$

$27 \sqrt{98}$

Step 4

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 4.1

Factor $49$ out of $98$ .

$27 \sqrt{49 (2)}$

Step 4.2

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

$27 \sqrt{7^{2} \cdot 2}$

$27 \sqrt{7^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$27 (7 \sqrt{2})$

Step 6

Multiply $7$ by $27$ .

$189 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$189 \sqrt{2}$

Decimal Form:

$267.28636328 \dots$

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