Solve 7/7sqrt{2^5}

$$\frac { 7 } { 7 \sqrt { 2 ^ { 5 } } }$$

Evaluate

$$\frac{\sqrt{2}}{8}\approx 0.176776695$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\frac{7}{7\sqrt{32}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{7}{7\times 4\sqrt{2}}$$

Multiply 7 and 4 to get 28.

$$\frac{7}{28\sqrt{2}}$$

Rationalize the denominator of \frac{7}{28\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7\sqrt{2}}{28\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7\sqrt{2}}{28\times 2}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\sqrt{2}}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{\sqrt{2}}{8}$$