Simplify square root of 25* square root of 50

$\sqrt{25} \cdot \sqrt{50}$

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

$\sqrt{5^{2}} \cdot \sqrt{50}$

Pull terms out from under the radical, assuming positive real numbers.

$5 \cdot \sqrt{50}$

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

Factor $25$ out of $50$ .

$5 \cdot \sqrt{25 (2)}$

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $5$ .

$25 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$25 \sqrt{2}$

Decimal Form:

$35.35533905 \dots$