Solve x=3/5+1/sqrt{2}+sqrt{3}

$$x= \frac{ 3 }{ 5 } + \frac{ 1 }{ \sqrt{ 2 } } + \sqrt{ 3 }$$

Solve for x

$$x=\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{3}{5}\approx 3.039157589$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$x=\frac{3}{5}+\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{3}$$

The square of \sqrt{2} is 2.

$$x=\frac{3}{5}+\frac{\sqrt{2}}{2}+\sqrt{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{3}{5} times \frac{2}{2}. Multiply \frac{\sqrt{2}}{2} times \frac{5}{5}.

$$x=\frac{3\times 2}{10}+\frac{5\sqrt{2}}{10}+\sqrt{3}$$

Since \frac{3\times 2}{10} and \frac{5\sqrt{2}}{10} have the same denominator, add them by adding their numerators.

$$x=\frac{3\times 2+5\sqrt{2}}{10}+\sqrt{3}$$

Do the multiplications in 3\times 2+5\sqrt{2}.

$$x=\frac{6+5\sqrt{2}}{10}+\sqrt{3}$$

Divide each term of 6+5\sqrt{2} by 10 to get \frac{3}{5}+\frac{1}{2}\sqrt{2}.

$$x=\frac{3}{5}+\frac{1}{2}\sqrt{2}+\sqrt{3}$$

Assign x

$$x≔\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{3}{5}$$