Simplify (2/3)/( square root of 9-(2/3)^2)

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

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{1}{\sqrt{9 - {(\frac{2}{3})}^{2}}}$

Combine fractions.

Combine.

$\frac{2 \cdot 1}{3 \sqrt{9 - {(\frac{2}{3})}^{2}}}$

Multiply $2$ by $1$ .

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

Simplify the denominator.

Apply the product rule to $\frac{2}{3}$ .

$\frac{2}{3 \sqrt{9 - \frac{2^{2}}{3^{2}}}}$

Raise $2$ to the power of $2$ .

$\frac{2}{3 \sqrt{9 - \frac{4}{3^{2}}}}$

Raise $3$ to the power of $2$ .

$\frac{2}{3 \sqrt{9 - \frac{4}{9}}}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{3 \sqrt{9 \cdot \frac{9}{9} - \frac{4}{9}}}$

Combine $9$ and $\frac{9}{9}$ .

$\frac{2}{3 \sqrt{\frac{9 \cdot 9}{9} - \frac{4}{9}}}$

Combine the numerators over the common denominator.

$\frac{2}{3 \sqrt{\frac{9 \cdot 9 - 4}{9}}}$

Simplify the numerator.

Multiply $9$ by $9$ .

$\frac{2}{3 \sqrt{\frac{81 - 4}{9}}}$

Subtract $4$ from $81$ .

$\frac{2}{3 \sqrt{\frac{77}{9}}}$

Rewrite $\sqrt{\frac{77}{9}}$ as $\frac{\sqrt{77}}{\sqrt{9}}$ .

$\frac{2}{3 \frac{\sqrt{77}}{\sqrt{9}}}$

Simplify the denominator.

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

$\frac{2}{3 \frac{\sqrt{77}}{\sqrt{3^{2}}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2}{3 \frac{\sqrt{77}}{3}}$

Combine $3$ and $\frac{\sqrt{77}}{3}$ .

$\frac{2}{\frac{3 \sqrt{77}}{3}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{3 \sqrt{77}}{3}$ by cancelling the common factors.

Cancel the common factor.

$\frac{2}{\frac{3 \sqrt{77}}{3}}$

Rewrite the expression.

$\frac{2}{\frac{\sqrt{77}}{1}}$

Divide $\sqrt{77}$ by $1$ .

$\frac{2}{\sqrt{77}}$

Multiply $\frac{2}{\sqrt{77}}$ by $\frac{\sqrt{77}}{\sqrt{77}}$ .

$\frac{2}{\sqrt{77}} \cdot \frac{\sqrt{77}}{\sqrt{77}}$

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{77}}$ by $\frac{\sqrt{77}}{\sqrt{77}}$ .

$\frac{2 \sqrt{77}}{\sqrt{77} \sqrt{77}}$

Raise $\sqrt{77}$ to the power of $1$ .

$\frac{2 \sqrt{77}}{{\sqrt{77}}^{1} \sqrt{77}}$

Raise $\sqrt{77}$ to the power of $1$ .

$\frac{2 \sqrt{77}}{{\sqrt{77}}^{1} {\sqrt{77}}^{1}}$

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

$\frac{2 \sqrt{77}}{{\sqrt{77}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{77}}{{\sqrt{77}}^{2}}$

Rewrite ${\sqrt{77}}^{2}$ as $77$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{77}$ as $77^{\frac{1}{2}}$ .

$\frac{2 \sqrt{77}}{{(77^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{77}}{77^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{77}}{77^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{77}}{77^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{77}}{77^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{77}}{77}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{77}}{77}$

Decimal Form:

$0.22792115 \dots$

Simplify (2/3)/( square root of 9-(2/3)^2)

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