Solve 110/7sqrt{32}

$$1 \frac{ 10 }{ 7 \sqrt{ 32 } }$$

Evaluate

$$\frac{5\sqrt{2}}{28}\approx 0.252538136$$

Solution Steps

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}.

$$1\times \frac{10}{7\times 4\sqrt{2}}$$

Multiply 7 and 4 to get 28.

$$1\times \frac{10}{28\sqrt{2}}$$

Rationalize the denominator of \frac{10}{28\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$1\times \frac{10\sqrt{2}}{28\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$1\times \frac{10\sqrt{2}}{28\times 2}$$

Cancel out 2 in both numerator and denominator.

$$1\times \frac{5\sqrt{2}}{2\times 14}$$

Multiply 2 and 14 to get 28.

$$1\times \frac{5\sqrt{2}}{28}$$

Express 1\times \frac{5\sqrt{2}}{28} as a single fraction.

$$\frac{5\sqrt{2}}{28}$$