Evaluate 4 square root of 50* square root of 80

$4 \sqrt{50} \cdot \sqrt{80}$

Rewrite $50$ as $5^{2} \cdot 2$ .

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Factor $25$ out of $50$ .

$4 \sqrt{25 (2)} \cdot \sqrt{80}$

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{5^{2} \cdot 2} \cdot \sqrt{80}$

Pull terms out from under the radical.

$4 (5 \sqrt{2}) \cdot \sqrt{80}$

Multiply $5$ by $4$ .

$20 \sqrt{2} \cdot \sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

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Factor $16$ out of $80$ .

$20 \sqrt{2} \cdot \sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$20 \sqrt{2} \cdot \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$20 \sqrt{2} \cdot (4 \sqrt{5})$

Multiply $20 \sqrt{2} (4 \sqrt{5})$ .

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Multiply $4$ by $20$ .

$80 \sqrt{2} \sqrt{5}$

Combine using the product rule for radicals.

$80 \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$80 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{10}$

Decimal Form:

$252.98221281 \dots$

Evaluate 4 square root of 50* square root of 80

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