Solve 2sqrt{1+19*10^-6*20}

$$2 \sqrt{ 1+19 \times { 10 }^{ -6 } \times 20 }$$

Evaluate

$$\frac{\sqrt{250095}}{250}\approx 2.000379964$$

Solution Steps

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$2\sqrt{1+19\times \frac{1}{1000000}\times 20}$$

Multiply 19 and \frac{1}{1000000} to get \frac{19}{1000000}.

$$2\sqrt{1+\frac{19}{1000000}\times 20}$$

Multiply \frac{19}{1000000} and 20 to get \frac{19}{50000}.

$$2\sqrt{1+\frac{19}{50000}}$$

Add 1 and \frac{19}{50000} to get \frac{50019}{50000}.

$$2\sqrt{\frac{50019}{50000}}$$

Rewrite the square root of the division \sqrt{\frac{50019}{50000}} as the division of square roots \frac{\sqrt{50019}}{\sqrt{50000}}.

$$2\times \frac{\sqrt{50019}}{\sqrt{50000}}$$

Factor 50000=100^{2}\times 5. Rewrite the square root of the product \sqrt{100^{2}\times 5} as the product of square roots \sqrt{100^{2}}\sqrt{5}. Take the square root of 100^{2}.

$$2\times \frac{\sqrt{50019}}{100\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{50019}}{100\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$2\times \frac{\sqrt{50019}\sqrt{5}}{100\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$2\times \frac{\sqrt{50019}\sqrt{5}}{100\times 5}$$

To multiply \sqrt{50019} and \sqrt{5}, multiply the numbers under the square root.

$$2\times \frac{\sqrt{250095}}{100\times 5}$$

Multiply 100 and 5 to get 500.

$$2\times \frac{\sqrt{250095}}{500}$$

Cancel out 500, the greatest common factor in 2 and 500.

$$\frac{\sqrt{250095}}{250}$$