Solve {left(2sqrt{3/8}right)}^2

$${ \left(2 \sqrt{ \frac{ 3 }{ 8 } } \right) }^{ 2 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{8}} as the division of square roots \frac{\sqrt{3}}{\sqrt{8}}.

$$\left(2\times \frac{\sqrt{3}}{\sqrt{8}}\right)^{2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

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

Cancel out 4, the greatest common factor in 2 and 4.

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

To raise \frac{\sqrt{6}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

The square of \sqrt{6} is 6.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$