Solve sqrt[4]{2/105/102/105/10}

$$\sqrt[ 4 ]{ \frac{ 2 }{ 10 } \frac{ 5 }{ 10 } \frac{ 2 }{ 10 } \frac{ 5 }{ 10 } }$$

Evaluate

$$\frac{\sqrt{10}}{10}\approx 0.316227766$$

Solution Steps

Multiply \frac{2}{10} and \frac{2}{10} to get \left(\frac{2}{10}\right)^{2}.

$$\sqrt[4]{\left(\frac{2}{10}\right)^{2}\times \frac{5}{10}\times \frac{5}{10}}$$

Multiply \frac{5}{10} and \frac{5}{10} to get \left(\frac{5}{10}\right)^{2}.

$$\sqrt[4]{\left(\frac{2}{10}\right)^{2}\times \left(\frac{5}{10}\right)^{2}}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt[4]{\left(\frac{1}{5}\right)^{2}\times \left(\frac{5}{10}\right)^{2}}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\sqrt[4]{\frac{1}{25}\times \left(\frac{5}{10}\right)^{2}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\sqrt[4]{\frac{1}{25}\times \left(\frac{1}{2}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\sqrt[4]{\frac{1}{25}\times \frac{1}{4}}$$

Multiply \frac{1}{25} and \frac{1}{4} to get \frac{1}{100}.

$$\sqrt[4]{\frac{1}{100}}$$