Solve 10/sqrt{32}

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

Evaluate

$$\frac{5\sqrt{2}}{4}\approx 1.767766953$$

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}.

$$\frac{10}{4\sqrt{2}}$$

Rationalize the denominator of \frac{10}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{10\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{5\sqrt{2}}{4}$$