Simplify 6/( square root of 3)*( square root of 2)/( square root of 3)

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

Step 1

Multiply $\frac{6}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 2

Combine and simplify the denominator.

Multiply $\frac{6}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Cancel the common factor of $\sqrt{3}$ .

Factor $\sqrt{3}$ out of $6 \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Combine $\frac{6}{3}$ and $\sqrt{2}$ .

$\frac{6 \sqrt{2}}{3}$

Step 5

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{2}$ .

$\frac{3 (2 \sqrt{2})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{2})}{3 (1)}$

Cancel the common factor.

$\frac{3 (2 \sqrt{2})}{3 \cdot 1}$

Rewrite the expression.

$\frac{2 \sqrt{2}}{1}$

Divide $2 \sqrt{2}$ by $1$ .

$2 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

Simplify 6/( square root of 3)*( square root of 2)/( square root of 3)

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