Solve 2.77^3/T^2=1/365^2

$$\frac { 2.77 ^ { 3 } } { T ^ { 2 } } = \frac { 1 } { 365 ^ { 2 } }$$

Solve for T

$$T = \frac{20221 \sqrt{277}}{200} \approx 1682.722562969$$

$$T = -\frac{20221 \sqrt{277}}{200} \approx -1682.722562969$$

Steps by Finding Square Root

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T^{2}.

$$2.77^{3}=\frac{1}{133225}T^{2}$$

Calculate 2.77 to the power of 3 and get 21.253933.

$$21.253933=\frac{1}{133225}T^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{133225}T^{2}=21.253933$$

Multiply both sides by 133225, the reciprocal of \frac{1}{133225}.

$$T^{2}=21.253933\times 133225$$

Multiply 21.253933 and 133225 to get 2831555.223925.

$$T^{2}=2831555.223925$$

Take the square root of both sides of the equation.

$$T=\frac{20221\sqrt{277}}{200} T=-\frac{20221\sqrt{277}}{200}$$

Steps Using the Quadratic Formula

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T^{2}.

$$2.77^{3}=\frac{1}{133225}T^{2}$$

Calculate 2.77 to the power of 3 and get 21.253933.

$$21.253933=\frac{1}{133225}T^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{133225}T^{2}=21.253933$$

Subtract 21.253933 from both sides.

$$\frac{1}{133225}T^{2}-21.253933=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{133225} for a, 0 for b, and -21.253933 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$T=\frac{0±\sqrt{0^{2}-4\times \frac{1}{133225}\left(-21.253933\right)}}{2\times \frac{1}{133225}}$$

Square 0.

$$T=\frac{0±\sqrt{-4\times \frac{1}{133225}\left(-21.253933\right)}}{2\times \frac{1}{133225}}$$

Multiply -4 times \frac{1}{133225}.

$$T=\frac{0±\sqrt{-\frac{4}{133225}\left(-21.253933\right)}}{2\times \frac{1}{133225}}$$

Multiply -\frac{4}{133225} times -21.253933 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$T=\frac{0±\sqrt{\frac{21253933}{33306250000}}}{2\times \frac{1}{133225}}$$

Take the square root of \frac{21253933}{33306250000}.

$$T=\frac{0±\frac{277\sqrt{277}}{182500}}{2\times \frac{1}{133225}}$$

Multiply 2 times \frac{1}{133225}.

$$T=\frac{0±\frac{277\sqrt{277}}{182500}}{\frac{2}{133225}}$$

Now solve the equation T=\frac{0±\frac{277\sqrt{277}}{182500}}{\frac{2}{133225}} when ± is plus.

$$T=\frac{20221\sqrt{277}}{200}$$

Now solve the equation T=\frac{0±\frac{277\sqrt{277}}{182500}}{\frac{2}{133225}} when ± is minus.

$$T=-\frac{20221\sqrt{277}}{200}$$

The equation is now solved.

$$T=\frac{20221\sqrt{277}}{200} T=-\frac{20221\sqrt{277}}{200}$$