Solve (3*8)/25sqrt{8}+sqrt{3}=

$$\frac { ( 3 \times 8 ) } { 25 \sqrt { 8 } } + \sqrt { 3 } =$$

Evaluate

$$\frac{6\sqrt{2}}{25}+\sqrt{3}\approx 2.071462063$$

Short Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{24}{25\sqrt{8}}+\sqrt{3}$$

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}.

$$\frac{24}{25\times 2\sqrt{2}}+\sqrt{3}$$

Multiply 25 and 2 to get 50.

$$\frac{24}{50\sqrt{2}}+\sqrt{3}$$

Rationalize the denominator of \frac{24}{50\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{24\sqrt{2}}{50\left(\sqrt{2}\right)^{2}}+\sqrt{3}$$

The square of \sqrt{2} is 2.

$$\frac{24\sqrt{2}}{50\times 2}+\sqrt{3}$$

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{6\sqrt{2}}{25}+\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3} times \frac{25}{25}.

$$\frac{6\sqrt{2}}{25}+\frac{25\sqrt{3}}{25}$$

Since \frac{6\sqrt{2}}{25} and \frac{25\sqrt{3}}{25} have the same denominator, add them by adding their numerators.

$$\frac{6\sqrt{2}+25\sqrt{3}}{25}$$

Factor

$$\frac{6 \sqrt{2} + 25 \sqrt{3}}{25} = 2.07146206253842$$