Simplify square root of 10* square root of 5

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

Step 1

Combine using the product rule for radicals.

$\sqrt{10 \cdot 5}$

Step 2

Multiply $10$ by $5$ .

$\sqrt{50}$

Step 3

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

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

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

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

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

Step 4

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

Related Questions