Solve B*sqrt{100/16}*sqrt{14}*3/2

$$B \cdot \sqrt { \frac { 100 } { 16 } } \times \sqrt { 14 } \times \frac { 3 } { 2 }$$

Evaluate

$$\frac{15\sqrt{14}B}{4}$$

Solution Steps

Reduce the fraction \frac{100}{16} to lowest terms by extracting and canceling out 4.

$$B\sqrt{\frac{25}{4}}\sqrt{14}\times \frac{3}{2}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$B\times \frac{5}{2}\sqrt{14}\times \frac{3}{2}$$

Multiply \frac{5}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$B\times \frac{5\times 3}{2\times 2}\sqrt{14}$$

Do the multiplications in the fraction \frac{5\times 3}{2\times 2}.

$$B\times \frac{15}{4}\sqrt{14}$$

Differentiate w.r.t. B

$$\frac{15 \sqrt{14}}{4} = 14.03121520040228$$