Solve frac{1*10^-8+sqrt{1*10^-16+4*10^-14}}{2}=

$$\frac { 1 \cdot 10 ^ { - 8 } + \sqrt { 1 \cdot 10 ^ { - 16 } + 4 \cdot 10 ^ { - 14 } } } { 2 } =$$

Evaluate

$$\frac{\sqrt{401}+1}{200000000}\approx 0.000000105$$

Solution Steps

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\frac{1\times \frac{1}{100000000}+\sqrt{1\times 10^{-16}+4\times 10^{-14}}}{2}$$

Multiply 1 and \frac{1}{100000000} to get \frac{1}{100000000}.

$$\frac{\frac{1}{100000000}+\sqrt{1\times 10^{-16}+4\times 10^{-14}}}{2}$$

Calculate 10 to the power of -16 and get \frac{1}{10000000000000000}.

$$\frac{\frac{1}{100000000}+\sqrt{1\times \frac{1}{10000000000000000}+4\times 10^{-14}}}{2}$$

Multiply 1 and \frac{1}{10000000000000000} to get \frac{1}{10000000000000000}.

$$\frac{\frac{1}{100000000}+\sqrt{\frac{1}{10000000000000000}+4\times 10^{-14}}}{2}$$

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$\frac{\frac{1}{100000000}+\sqrt{\frac{1}{10000000000000000}+4\times \frac{1}{100000000000000}}}{2}$$

Multiply 4 and \frac{1}{100000000000000} to get \frac{1}{25000000000000}.

$$\frac{\frac{1}{100000000}+\sqrt{\frac{1}{10000000000000000}+\frac{1}{25000000000000}}}{2}$$

Add \frac{1}{10000000000000000} and \frac{1}{25000000000000} to get \frac{401}{10000000000000000}.

$$\frac{\frac{1}{100000000}+\sqrt{\frac{401}{10000000000000000}}}{2}$$

Rewrite the square root of the division \sqrt{\frac{401}{10000000000000000}} as the division of square roots \frac{\sqrt{401}}{\sqrt{10000000000000000}}.

$$\frac{\frac{1}{100000000}+\frac{\sqrt{401}}{\sqrt{10000000000000000}}}{2}$$

Calculate the square root of 10000000000000000 and get 100000000.

$$\frac{\frac{1}{100000000}+\frac{\sqrt{401}}{100000000}}{2}$$

Since \frac{1}{100000000} and \frac{\sqrt{401}}{100000000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+\sqrt{401}}{100000000}}{2}$$

Express \frac{\frac{1+\sqrt{401}}{100000000}}{2} as a single fraction.

$$\frac{1+\sqrt{401}}{100000000\times 2}$$

Multiply 100000000 and 2 to get 200000000.

$$\frac{1+\sqrt{401}}{200000000}$$

Factor

$$\frac{\sqrt{401} + 1}{200000000} = 1.0512492197250394 \times 10^{-7}$$