Evaluate 1/( square root of 3/2)

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

Simplify the denominator.

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

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

Multiply $\frac{\sqrt{3}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$\frac{1}{\frac{\sqrt{6}}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{2}{\sqrt{6}}$

Multiply $\frac{2}{\sqrt{6}}$ by $1$ .

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

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

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

Raise $\sqrt{6}$ to the power of $1$ .

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

Raise $\sqrt{6}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.81649658 \dots$

Evaluate 1/( square root of 3/2)

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