Simplify square root of 3(3+ square root of 5)

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

Simplify terms.

Apply the distributive property.

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

Move $3$ to the left of $\sqrt{3}$ .

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

Combine using the product rule for radicals.

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

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

Multiply $3$ by $5$ .

$3 \sqrt{3} + \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3} + \sqrt{15}$

Decimal Form:

$9.06913576 \dots$

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