Solve 3*sqrt{3/2}*8^2

$$3 \times \sqrt{ \frac{ 3 }{ 2 } } \times { 8 }^{ 2 }$$

Evaluate

$$96\sqrt{6}\approx 235.151015307$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$3\times \frac{\sqrt{3}}{\sqrt{2}}\times 8^{2}$$

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

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

The square of \sqrt{2} is 2.

$$3\times \frac{\sqrt{3}\sqrt{2}}{2}\times 8^{2}$$

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

$$3\times \frac{\sqrt{6}}{2}\times 8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$3\times \frac{\sqrt{6}}{2}\times 64$$

Multiply 3 and 64 to get 192.

$$192\times \frac{\sqrt{6}}{2}$$

Cancel out 2, the greatest common factor in 192 and 2.

$$96\sqrt{6}$$