Solve 5/2divfrac{sqrt{50}}{2}

$$\frac{ 5 }{ 2 } \div \frac{ \sqrt{ 50 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Divide \frac{5}{2} by \frac{\sqrt{50}}{2} by multiplying \frac{5}{2} by the reciprocal of \frac{\sqrt{50}}{2}.

$$\frac{5\times 2}{2\sqrt{50}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

Rationalize the denominator of \frac{5}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 5 in both numerator and denominator.

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