Solve (frac{sqrt{2}x}{sqrt{3}}x)^2

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

Evaluate

$$\frac{2x^{4}}{3}$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\left(\frac{\sqrt{2}x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}x\right)^{2}$$

The square of \sqrt{3} is 3.

$$\left(\frac{\sqrt{2}x\sqrt{3}}{3}x\right)^{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\left(\frac{\sqrt{6}x}{3}x\right)^{2}$$

Express \frac{\sqrt{6}x}{3}x as a single fraction.

$$\left(\frac{\sqrt{6}xx}{3}\right)^{2}$$

To raise \frac{\sqrt{6}xx}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{6}xx\right)^{2}}{3^{2}}$$

Multiply x and x to get x^{2}.

$$\frac{\left(\sqrt{6}x^{2}\right)^{2}}{3^{2}}$$

Expand \left(\sqrt{6}x^{2}\right)^{2}.

$$\frac{\left(\sqrt{6}\right)^{2}\left(x^{2}\right)^{2}}{3^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(\sqrt{6}\right)^{2}x^{4}}{3^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{6x^{4}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6x^{4}}{9}$$

Divide 6x^{4} by 9 to get \frac{2}{3}x^{4}.

$$\frac{2}{3}x^{4}$$

Expand

$$\frac{2x^{4}}{3}$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\left(\frac{\sqrt{2}x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}x\right)^{2}$$

The square of \sqrt{3} is 3.

$$\left(\frac{\sqrt{2}x\sqrt{3}}{3}x\right)^{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\left(\frac{\sqrt{6}x}{3}x\right)^{2}$$

Express \frac{\sqrt{6}x}{3}x as a single fraction.

$$\left(\frac{\sqrt{6}xx}{3}\right)^{2}$$

To raise \frac{\sqrt{6}xx}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{6}xx\right)^{2}}{3^{2}}$$

Multiply x and x to get x^{2}.

$$\frac{\left(\sqrt{6}x^{2}\right)^{2}}{3^{2}}$$

Expand \left(\sqrt{6}x^{2}\right)^{2}.

$$\frac{\left(\sqrt{6}\right)^{2}\left(x^{2}\right)^{2}}{3^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(\sqrt{6}\right)^{2}x^{4}}{3^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{6x^{4}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6x^{4}}{9}$$

Divide 6x^{4} by 9 to get \frac{2}{3}x^{4}.

$$\frac{2}{3}x^{4}$$