Evaluate square root of 5* square root of 35

$\sqrt{5} \cdot \sqrt{35}$

Step 1

Combine using the product rule for radicals.

$\sqrt{5 \cdot 35}$

Step 2

Multiply $5$ by $35$ .

$\sqrt{175}$

Step 3

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$\sqrt{25 (7)}$

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

$\sqrt{5^{2} \cdot 7}$

$\sqrt{5^{2} \cdot 7}$

Step 4

Pull terms out from under the radical.

$5 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{7}$

Decimal Form:

$13.22875655 \dots$

Related Questions