Solve 8sqrt{10}:sqrt{2}

$$8 \sqrt { 10 } : \sqrt { 2 }$$

Evaluate

$$8\sqrt{5}\approx 17.88854382$$

Solution Steps

Rationalize the denominator of \frac{8\sqrt{10}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{8\sqrt{10}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{8\sqrt{10}\sqrt{2}}{2}$$

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}.

$$\frac{8\sqrt{2}\sqrt{5}\sqrt{2}}{2}$$

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

$$\frac{8\times 2\sqrt{5}}{2}$$

Cancel out 2 and 2.

$$8\sqrt{5}$$