Simplify square root of 2( square root of 8+ square root of 6)

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

Simplify each term.

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

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Apply the distributive property.

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

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

Raise $\sqrt{2}$ to the power of $1$ .

$2 ({\sqrt{2}}^{1} \sqrt{2}) + \sqrt{2} \sqrt{6}$

Raise $\sqrt{2}$ to the power of $1$ .

$2 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) + \sqrt{2} \sqrt{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 {\sqrt{2}}^{1 + 1} + \sqrt{2} \sqrt{6}$

Add $1$ and $1$ .

$2 {\sqrt{2}}^{2} + \sqrt{2} \sqrt{6}$

Combine using the product rule for radicals.

$2 {\sqrt{2}}^{2} + \sqrt{2 \cdot 6}$

Simplify each term.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$2 {(2^{\frac{1}{2}})}^{2} + \sqrt{2 \cdot 6}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{\frac{1}{2} \cdot 2} + \sqrt{2 \cdot 6}$

Combine $\frac{1}{2}$ and $2$ .

$2 \cdot 2^{\frac{2}{2}} + \sqrt{2 \cdot 6}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \cdot 2^{\frac{2}{2}} + \sqrt{2 \cdot 6}$

Rewrite the expression.

$2 \cdot 2^{1} + \sqrt{2 \cdot 6}$

Evaluate the exponent.

$2 \cdot 2 + \sqrt{2 \cdot 6}$

Multiply $2$ by $2$ .

$4 + \sqrt{2 \cdot 6}$

Multiply $2$ by $6$ .

$4 + \sqrt{12}$

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

Factor $4$ out of $12$ .

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

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

$4 + \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$4 + 2 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$4 + 2 \sqrt{3}$

Decimal Form:

$7.46410161 \dots$

Simplify square root of 2( square root of 8+ square root of 6)

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