Solve T=124.32-35/frac{37.74{sqrt{52}}}

$$T = \frac { 124.32 - 35 } { \frac { 37.74 } { \sqrt { 52 } } }$$

Solve for T

$$T = \frac{8932 \sqrt{13}}{1887} \approx 17.066658184$$

Steps for Solving Linear Equation

Subtract 35 from 124.32 to get 89.32.

$$T=\frac{89.32}{\frac{37.74}{\sqrt{52}}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$T=\frac{89.32}{\frac{37.74}{2\sqrt{13}}}$$

Rationalize the denominator of \frac{37.74}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$T=\frac{89.32}{\frac{37.74\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}}$$

The square of \sqrt{13} is 13.

$$T=\frac{89.32}{\frac{37.74\sqrt{13}}{2\times 13}}$$

Multiply 2 and 13 to get 26.

$$T=\frac{89.32}{\frac{37.74\sqrt{13}}{26}}$$

Divide 37.74\sqrt{13} by 26 to get \frac{1887}{1300}\sqrt{13}.

$$T=\frac{89.32}{\frac{1887}{1300}\sqrt{13}}$$

Rationalize the denominator of \frac{89.32}{\frac{1887}{1300}\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$T=\frac{89.32\sqrt{13}}{\frac{1887}{1300}\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$T=\frac{89.32\sqrt{13}}{\frac{1887}{1300}\times 13}$$

Multiply \frac{1887}{1300} and 13 to get 18.87.

$$T=\frac{89.32\sqrt{13}}{18.87}$$

Divide 89.32\sqrt{13} by 18.87 to get \frac{8932}{1887}\sqrt{13}.

$$T=\frac{8932}{1887}\sqrt{13}$$

Assign T

$$T≔\frac{8932\sqrt{13}}{1887}$$