Solve 156div95*141*sqrt{4/314}*2=

$$156 \div 95 \times 141 \times \sqrt{ \frac{ 4 }{ 314 } } \times 2=$$

Evaluate

$$\frac{43992\sqrt{314}}{14915}\approx 52.265519684$$

Solution Steps

Multiply 2 and 141 to get 282.

$$282\times \frac{156}{95}\sqrt{\frac{4}{314}}$$

Express 282\times \frac{156}{95} as a single fraction.

$$\frac{282\times 156}{95}\sqrt{\frac{4}{314}}$$

Multiply 282 and 156 to get 43992.

$$\frac{43992}{95}\sqrt{\frac{4}{314}}$$

Reduce the fraction \frac{4}{314} to lowest terms by extracting and canceling out 2.

$$\frac{43992}{95}\sqrt{\frac{2}{157}}$$

Rewrite the square root of the division \sqrt{\frac{2}{157}} as the division of square roots \frac{\sqrt{2}}{\sqrt{157}}.

$$\frac{43992}{95}\times \frac{\sqrt{2}}{\sqrt{157}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{43992}{95}\times \frac{\sqrt{2}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{43992}{95}\times \frac{\sqrt{2}\sqrt{157}}{157}$$

To multiply \sqrt{2} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{43992}{95}\times \frac{\sqrt{314}}{157}$$

Multiply \frac{43992}{95} times \frac{\sqrt{314}}{157} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43992\sqrt{314}}{95\times 157}$$

Multiply 95 and 157 to get 14915.

$$\frac{43992\sqrt{314}}{14915}$$