Solve 40/216*1/10^21=t^2

$$\frac { 40 } { 216 } \times \frac { 1 } { 10 ^ { 21 } } = t ^ { 2 }$$

Solve for t

$$t=\frac{\sqrt{6}}{180000000000}\approx 1.360827635 \cdot 10^{-11}$$

$$t=-\frac{\sqrt{6}}{180000000000}\approx -1.360827635 \cdot 10^{-11}$$

Steps by Finding Square Root

Reduce the fraction \frac{40}{216} to lowest terms by extracting and canceling out 8.

$$\frac{5}{27}\times \frac{1}{10^{21}}=t^{2}$$

Calculate 10 to the power of 21 and get 1000000000000000000000.

$$\frac{5}{27}\times \frac{1}{1000000000000000000000}=t^{2}$$

Multiply \frac{5}{27} and \frac{1}{1000000000000000000000} to get \frac{1}{5400000000000000000000}.

$$\frac{1}{5400000000000000000000}=t^{2}$$

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

$$t^{2}=\frac{1}{5400000000000000000000}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{6}}{180000000000} t=-\frac{\sqrt{6}}{180000000000}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{40}{216} to lowest terms by extracting and canceling out 8.

$$\frac{5}{27}\times \frac{1}{10^{21}}=t^{2}$$

Calculate 10 to the power of 21 and get 1000000000000000000000.

$$\frac{5}{27}\times \frac{1}{1000000000000000000000}=t^{2}$$

Multiply \frac{5}{27} and \frac{1}{1000000000000000000000} to get \frac{1}{5400000000000000000000}.

$$\frac{1}{5400000000000000000000}=t^{2}$$

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

$$t^{2}=\frac{1}{5400000000000000000000}$$

Subtract \frac{1}{5400000000000000000000} from both sides.

$$t^{2}-\frac{1}{5400000000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{5400000000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{5400000000000000000000}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{1}{5400000000000000000000}\right)}}{2}$$

Multiply -4 times -\frac{1}{5400000000000000000000}.

$$t=\frac{0±\sqrt{\frac{1}{1350000000000000000000}}}{2}$$

Take the square root of \frac{1}{1350000000000000000000}.

$$t=\frac{0±\frac{\sqrt{6}}{90000000000}}{2}$$

Now solve the equation t=\frac{0±\frac{\sqrt{6}}{90000000000}}{2} when ± is plus.

$$t=\frac{\sqrt{6}}{180000000000}$$

Now solve the equation t=\frac{0±\frac{\sqrt{6}}{90000000000}}{2} when ± is minus.

$$t=-\frac{\sqrt{6}}{180000000000}$$

The equation is now solved.

$$t=\frac{\sqrt{6}}{180000000000} t=-\frac{\sqrt{6}}{180000000000}$$