Pre-Algebra Examples

$\sqrt{160^{2} + 480^{2} + 160 \cdot 480 \cdot \sqrt{3}}$

Step 1

Raise $160$ to the power of $2$ .

$\sqrt{25600 + 480^{2} + 160 \cdot 480 \cdot \sqrt{3}}$

Step 2

Raise $480$ to the power of $2$ .

$\sqrt{25600 + 230400 + 160 \cdot 480 \cdot \sqrt{3}}$

Step 3

Multiply $160$ by $480$ .

$\sqrt{25600 + 230400 + 76800 \cdot \sqrt{3}}$

Step 4

Add $25600$ and $230400$ .

$\sqrt{256000 + 76800 \sqrt{3}}$

Step 5

Rewrite $256000 + 76800 \sqrt{3}$ as $160^{2} (10 + 3 \sqrt{3})$ .

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Step 5.1

Factor $25600$ out of $256000$ .

$\sqrt{25600 (10) + 76800 \sqrt{3}}$

Step 5.2

Factor $25600$ out of $76800 \sqrt{3}$ .

$\sqrt{25600 (10) + 25600 (3 \sqrt{3})}$

Step 5.3

Factor $25600$ out of $25600 (10) + 25600 (3 \sqrt{3})$ .

$\sqrt{25600 (10 + 3 \sqrt{3})}$

Step 5.4

Rewrite $25600$ as $160^{2}$ .

$\sqrt{160^{2} (10 + 3 \sqrt{3})}$

Step 6

Pull terms out from under the radical.

$160 \sqrt{10 + 3 \sqrt{3}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$160 \sqrt{10 + 3 \sqrt{3}}$

Decimal Form:

$623.71588245 \dots$