Solve 50*10*sqrt{3/2}

$$50 \times 10 \times \sqrt{ \frac{ 3 }{ 2 } }$$

Evaluate

$$250\sqrt{6}\approx 612.372435696$$

Solution Steps

Multiply 10 and 50 to get 500.

$$500\sqrt{\frac{3}{2}}$$

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

$$500\times \frac{\sqrt{3}}{\sqrt{2}}$$

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

$$500\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$500\times \frac{\sqrt{3}\sqrt{2}}{2}$$

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

$$500\times \frac{\sqrt{6}}{2}$$

Cancel out 2, the greatest common factor in 500 and 2.

$$250\sqrt{6}$$