Simplify 2 square root of 3( square root of 6- square root of 3)

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $2 \sqrt{3} \sqrt{6}$ .

Combine using the product rule for radicals.

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

Multiply $6$ by $3$ .

$2 \sqrt{18} + 2 \sqrt{3} (- \sqrt{3})$

Step 3

Multiply $2 \sqrt{3} (- \sqrt{3})$ .

Multiply $- 1$ by $2$ .

$2 \sqrt{18} - 2 \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$2 \sqrt{18} - 2 ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$2 \sqrt{18} - 2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$2 \sqrt{18} - 2 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$2 \sqrt{18} - 2 {\sqrt{3}}^{2}$

Step 4

Simplify each term.

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

Factor $9$ out of $18$ .

$2 \sqrt{9 (2)} - 2 {\sqrt{3}}^{2}$

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

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

Pull terms out from under the radical.

$2 (3 \sqrt{2}) - 2 {\sqrt{3}}^{2}$

Multiply $3$ by $2$ .

$6 \sqrt{2} - 2 {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$6 \sqrt{2} - 2 {(3^{\frac{1}{2}})}^{2}$

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

$6 \sqrt{2} - 2 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$6 \sqrt{2} - 2 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 \sqrt{2} - 2 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$6 \sqrt{2} - 2 \cdot 3^{1}$

Evaluate the exponent.

$6 \sqrt{2} - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$6 \sqrt{2} - 6$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2} - 6$

Decimal Form:

$2.48528137 \dots$

Simplify 2 square root of 3( square root of 6- square root of 3)

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