Solve 156div95*1.41*sqrt{4/3.14}*2=

$$156 \div 95 \times 1.41 \times \sqrt{ \frac{ 4 }{ 3.14 } } \times 2=$$

Evaluate

$$\frac{21996\sqrt{314}}{74575}\approx 5.226551968$$

Solution Steps

Multiply 1.41 and 2 to get 2.82.

$$2.82\times \frac{156}{95}\sqrt{\frac{4}{3.14}}$$

Convert decimal number 2.82 to fraction \frac{282}{100}. Reduce the fraction \frac{282}{100} to lowest terms by extracting and canceling out 2.

$$\frac{141}{50}\times \frac{156}{95}\sqrt{\frac{4}{3.14}}$$

Multiply \frac{141}{50} times \frac{156}{95} by multiplying numerator times numerator and denominator times denominator.

$$\frac{141\times 156}{50\times 95}\sqrt{\frac{4}{3.14}}$$

Do the multiplications in the fraction \frac{141\times 156}{50\times 95}.

$$\frac{21996}{4750}\sqrt{\frac{4}{3.14}}$$

Reduce the fraction \frac{21996}{4750} to lowest terms by extracting and canceling out 2.

$$\frac{10998}{2375}\sqrt{\frac{4}{3.14}}$$

Expand \frac{4}{3.14} by multiplying both numerator and the denominator by 100.

$$\frac{10998}{2375}\sqrt{\frac{400}{314}}$$

Reduce the fraction \frac{400}{314} to lowest terms by extracting and canceling out 2.

$$\frac{10998}{2375}\sqrt{\frac{200}{157}}$$

Rewrite the square root of the division \sqrt{\frac{200}{157}} as the division of square roots \frac{\sqrt{200}}{\sqrt{157}}.

$$\frac{10998}{2375}\times \frac{\sqrt{200}}{\sqrt{157}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{10998}{2375}\times \frac{10\sqrt{2}}{\sqrt{157}}$$

Rationalize the denominator of \frac{10\sqrt{2}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{10998}{2375}\times \frac{10\sqrt{2}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{10998}{2375}\times \frac{10\sqrt{2}\sqrt{157}}{157}$$

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

$$\frac{10998}{2375}\times \frac{10\sqrt{314}}{157}$$

Multiply \frac{10998}{2375} times \frac{10\sqrt{314}}{157} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10998\times 10\sqrt{314}}{2375\times 157}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\times 10998\sqrt{314}}{157\times 475}$$

Multiply 2 and 10998 to get 21996.

$$\frac{21996\sqrt{314}}{157\times 475}$$

Multiply 157 and 475 to get 74575.

$$\frac{21996\sqrt{314}}{74575}$$