Solve y=1/3sqrt{22-1}

$$y = \frac { 1 } { 3 \sqrt { 22 } - 1 }$$

Solve for y

$$y=\frac{3\sqrt{22}+1}{197}\approx 0.076503793$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{3\sqrt{22}-1} by multiplying numerator and denominator by 3\sqrt{22}+1.

$$y=\frac{3\sqrt{22}+1}{\left(3\sqrt{22}-1\right)\left(3\sqrt{22}+1\right)}$$

Consider \left(3\sqrt{22}-1\right)\left(3\sqrt{22}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$y=\frac{3\sqrt{22}+1}{\left(3\sqrt{22}\right)^{2}-1^{2}}$$

Expand \left(3\sqrt{22}\right)^{2}.

$$y=\frac{3\sqrt{22}+1}{3^{2}\left(\sqrt{22}\right)^{2}-1^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$y=\frac{3\sqrt{22}+1}{9\left(\sqrt{22}\right)^{2}-1^{2}}$$

The square of \sqrt{22} is 22.

$$y=\frac{3\sqrt{22}+1}{9\times 22-1^{2}}$$

Multiply 9 and 22 to get 198.

$$y=\frac{3\sqrt{22}+1}{198-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$y=\frac{3\sqrt{22}+1}{198-1}$$

Subtract 1 from 198 to get 197.

$$y=\frac{3\sqrt{22}+1}{197}$$

Divide each term of 3\sqrt{22}+1 by 197 to get \frac{3}{197}\sqrt{22}+\frac{1}{197}.

$$y=\frac{3}{197}\sqrt{22}+\frac{1}{197}$$

Assign y

$$y≔\frac{3\sqrt{22}+1}{197}$$