Solve frac{3sqrt{10}}{6sqrt{2}}

$$\frac { 3 \sqrt { 10 } } { 6 \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

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

Divide 2\sqrt{5} by 4 to get \frac{1}{2}\sqrt{5}.

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