Simplify square root of 6( square root of 18+ square root of 8)

$\sqrt{6} (\sqrt{18} + \sqrt{8})$

Simplify each term.

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

Factor $9$ out of $18$ .

$\sqrt{6} (\sqrt{9 (2)} + \sqrt{8})$

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

$\sqrt{6} (\sqrt{3^{2} \cdot 2} + \sqrt{8})$

$\sqrt{6} (\sqrt{3^{2} \cdot 2} + \sqrt{8})$

Pull terms out from under the radical.

$\sqrt{6} (3 \sqrt{2} + \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{6} (3 \sqrt{2} + \sqrt{4 (2)})$

Rewrite $4$ as $2^{2}$ .

$\sqrt{6} (3 \sqrt{2} + \sqrt{2^{2} \cdot 2})$

$\sqrt{6} (3 \sqrt{2} + \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$\sqrt{6} (3 \sqrt{2} + 2 \sqrt{2})$

$\sqrt{6} (3 \sqrt{2} + 2 \sqrt{2})$

Add $3 \sqrt{2}$ and $2 \sqrt{2}$ .

$\sqrt{6} (5 \sqrt{2})$

Multiply $\sqrt{6} (5 \sqrt{2})$ .

Combine using the product rule for radicals.

$5 \sqrt{6 \cdot 2}$

Multiply $6$ by $2$ .

$5 \sqrt{12}$

$5 \sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$5 \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$5 \sqrt{2^{2} \cdot 3}$

$5 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$5 (2 \sqrt{3})$

Multiply $2$ by $5$ .

$10 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{3}$

Decimal Form:

$17.32050807 \dots$

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