Solve frac{sqrt{3}}{7sqrt{2^5}}

$$\frac { \sqrt { 3 } } { 7 \sqrt { 2 ^ { 5 } } }$$

Evaluate

$$\frac{\sqrt{6}}{56}\approx 0.043740888$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\frac{\sqrt{3}}{7\sqrt{32}}$$

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}.

$$\frac{\sqrt{3}}{7\times 4\sqrt{2}}$$

Multiply 7 and 4 to get 28.

$$\frac{\sqrt{3}}{28\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{28\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{28\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{28\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{28\times 2}$$

Multiply 28 and 2 to get 56.

$$\frac{\sqrt{6}}{56}$$