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

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

Step 1

Combine $\sqrt{2}$ and $\sqrt{6}$ into a single radical.

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

Step 2

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 \sqrt{\frac{1}{3}}$

Step 3

Rewrite $\sqrt{\frac{1}{3}}$ as $\frac{\sqrt{1}}{\sqrt{3}}$ .

$3 \frac{\sqrt{1}}{\sqrt{3}}$

Step 4

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt{3}}$

Step 5

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 6

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$3 \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}$

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

$3 \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

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

$3 \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$3 \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 \frac{\sqrt{3}}{3^{1}}$

Evaluate the exponent.

$3 \frac{\sqrt{3}}{3}$

Step 7

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{\sqrt{3}}{3}$

Rewrite the expression.

$\sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

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

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