Solve frac{sqrt{3}}{2}*50sqrt{2}-50sqrt{2}

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

Evaluate

$$25\sqrt{2}\left(\sqrt{3}-2\right)\approx -9.473434549$$

Solution Steps

Cancel out 2, the greatest common factor in 50 and 2.

$$25\sqrt{3}\sqrt{2}-50\sqrt{2}$$

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

$$25\sqrt{6}-50\sqrt{2}$$

Factor

$$25 \sqrt{2} {(\sqrt{3} - 2)} = -9.473434549$$