Evaluate square root of 5( square root of 3+ square root of 7)

$\sqrt{5} (\sqrt{3} + \sqrt{7})$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt{5} \sqrt{3} + \sqrt{5} \sqrt{7}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 3} + \sqrt{5} \sqrt{7}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 3} + \sqrt{5 \cdot 7}$

Step 2

Simplify each term.

Multiply $5$ by $3$ .

$\sqrt{15} + \sqrt{5 \cdot 7}$

Multiply $5$ by $7$ .

$\sqrt{15} + \sqrt{35}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{15} + \sqrt{35}$

Decimal Form:

$9.78906312 \dots$