Solve frac{sqrt{sqrt{256}}}{sqrt{235^5}}

$$\frac { \sqrt { \sqrt { 256 } } } { \sqrt { 235 ^ { 5 } } }$$

Evaluate

$$\frac{4\sqrt{235}}{12977875}\approx 0.000004725$$

Solution Steps

Calculate the square root of 256 and get 16.

$$\frac{\sqrt{16}}{\sqrt{235^{5}}}$$

Calculate the square root of 16 and get 4.

$$\frac{4}{\sqrt{235^{5}}}$$

Calculate 235 to the power of 5 and get 716703146875.

$$\frac{4}{\sqrt{716703146875}}$$

Factor 716703146875=55225^{2}\times 235. Rewrite the square root of the product \sqrt{55225^{2}\times 235} as the product of square roots \sqrt{55225^{2}}\sqrt{235}. Take the square root of 55225^{2}.

$$\frac{4}{55225\sqrt{235}}$$

Rationalize the denominator of \frac{4}{55225\sqrt{235}} by multiplying numerator and denominator by \sqrt{235}.

$$\frac{4\sqrt{235}}{55225\left(\sqrt{235}\right)^{2}}$$

The square of \sqrt{235} is 235.

$$\frac{4\sqrt{235}}{55225\times 235}$$

Multiply 55225 and 235 to get 12977875.

$$\frac{4\sqrt{235}}{12977875}$$