Evaluate square root of 2/3- square root of 3/2

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

Simplify each term.

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

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

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

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

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

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

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

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

To write $\frac{\sqrt{6}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

To write $- \frac{\sqrt{6}}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $2$ to the left of $\sqrt{6}$ .

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

Multiply $3$ by $- 1$ .

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

Subtract $3 \sqrt{6}$ from $2 \sqrt{6}$ .

$\frac{- \sqrt{6}}{6}$

Move the negative in front of the fraction.

$- \frac{\sqrt{6}}{6}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{6}}{6}$

Decimal Form:

$- 0.40824829 \dots$

Evaluate square root of 2/3- square root of 3/2

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