Solve S=1/sqrt{2+4}

$$S = \frac { 1 } { \sqrt { 2 } + 4 }$$

Solve for S

$$S=-\frac{\sqrt{2}}{14}+\frac{2}{7}\approx 0.184699031$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{2}+4} by multiplying numerator and denominator by \sqrt{2}-4.

$$S=\frac{\sqrt{2}-4}{\left(\sqrt{2}+4\right)\left(\sqrt{2}-4\right)}$$

Consider \left(\sqrt{2}+4\right)\left(\sqrt{2}-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$S=\frac{\sqrt{2}-4}{\left(\sqrt{2}\right)^{2}-4^{2}}$$

Square \sqrt{2}. Square 4.

$$S=\frac{\sqrt{2}-4}{2-16}$$

Subtract 16 from 2 to get -14.

$$S=\frac{\sqrt{2}-4}{-14}$$

Multiply both numerator and denominator by -1.

$$S=\frac{-\sqrt{2}+4}{14}$$

Divide each term of -\sqrt{2}+4 by 14 to get -\frac{1}{14}\sqrt{2}+\frac{2}{7}.

$$S=-\frac{1}{14}\sqrt{2}+\frac{2}{7}$$

Assign S

$$S≔-\frac{\sqrt{2}}{14}+\frac{2}{7}$$