Solve frac{sqrt{8}}{sqrt{123}}+1

$$\frac { \sqrt { 8 } } { \sqrt { 123 } } + 1$$

Evaluate

$$\frac{2\sqrt{246}}{123}+1\approx 1.255030685$$

Short Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{123}}+1$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{123}} by multiplying numerator and denominator by \sqrt{123}.

$$\frac{2\sqrt{2}\sqrt{123}}{\left(\sqrt{123}\right)^{2}}+1$$

The square of \sqrt{123} is 123.

$$\frac{2\sqrt{2}\sqrt{123}}{123}+1$$

To multiply \sqrt{2} and \sqrt{123}, multiply the numbers under the square root.

$$\frac{2\sqrt{246}}{123}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{123}{123}.

$$\frac{2\sqrt{246}}{123}+\frac{123}{123}$$

Since \frac{2\sqrt{246}}{123} and \frac{123}{123} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{246}+123}{123}$$