Simplify square root of 3( square root of 6+a)

$\sqrt{3} (\sqrt{6} + a)$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt{3} \sqrt{6} + \sqrt{3} a$

Combine using the product rule for radicals.

$\sqrt{3 \cdot 6} + \sqrt{3} a$

$\sqrt{3 \cdot 6} + \sqrt{3} a$

Step 2

Simplify each term.

Multiply $3$ by $6$ .

$\sqrt{18} + \sqrt{3} a$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2)} + \sqrt{3} a$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2} + \sqrt{3} a$

$\sqrt{3^{2} \cdot 2} + \sqrt{3} a$

Pull terms out from under the radical.

$3 \sqrt{2} + \sqrt{3} a$

$3 \sqrt{2} + \sqrt{3} a$

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