Evaluate square root of 2* square root of 5* square root of 8

$\sqrt{2} \cdot \sqrt{5} \cdot \sqrt{8}$

Step 1

Combine using the product rule for radicals.

$\sqrt{2 \cdot 5} \cdot \sqrt{8}$

Step 2

Combine using the product rule for radicals.

$\sqrt{2 \cdot 5 \cdot 8}$

Step 3

Multiply.

Multiply $2$ by $5$ .

$\sqrt{10 \cdot 8}$

Multiply $10$ by $8$ .

$\sqrt{80}$

$\sqrt{80}$

Step 4

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

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

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

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

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

Step 5

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

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