Simplify square root of 10* square root of 20

$\sqrt{10} \cdot \sqrt{20}$

Step 1

Combine using the product rule for radicals.

$\sqrt{10 \cdot 20}$

Step 2

Multiply $10$ by $20$ .

$\sqrt{200}$

Step 3

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$\sqrt{100 (2)}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2}$

$\sqrt{10^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$10 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2}$

Decimal Form:

$14.14213562 \dots$

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