Simplify 5 square root of 2*4 square root of 10

$5 \sqrt{2} \cdot 4 \sqrt{10}$

Step 1

Multiply $5 \sqrt{2} (4 \sqrt{10})$ .

Multiply $4$ by $5$ .

$20 \sqrt{2} \sqrt{10}$

Combine using the product rule for radicals.

$20 \sqrt{10 \cdot 2}$

Multiply $10$ by $2$ .

$20 \sqrt{20}$

$20 \sqrt{20}$

Step 2

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$20 \sqrt{4 (5)}$

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

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

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

Step 3

Pull terms out from under the radical.

$20 (2 \sqrt{5})$

Step 4

Multiply $2$ by $20$ .

$40 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$40 \sqrt{5}$

Decimal Form:

$89.44271909 \dots$

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