Solve 1-sqrt{1-2*6.674*5.94/3.6*10^7*2.998*10^3}

$$1 - \sqrt { 1 - \frac { 2 \times 6.674 \times 5.94 } { 3.6 \times 10 ^ { 7 } \times 2.998 \times 10 ^ { 3 } } }$$

Evaluate

$$-\frac{\sqrt{2247000998349286210}}{1499000000}+1\approx 3.673149562 \cdot 10^{-10}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$1-\sqrt{1-\frac{2\times 6.674\times 5.94}{3.6\times 10^{10}\times 2.998}}$$

Multiply 2 and 6.674 to get 13.348.

$$1-\sqrt{1-\frac{13.348\times 5.94}{3.6\times 10^{10}\times 2.998}}$$

Multiply 13.348 and 5.94 to get 79.28712.

$$1-\sqrt{1-\frac{79.28712}{3.6\times 10^{10}\times 2.998}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$1-\sqrt{1-\frac{79.28712}{3.6\times 10000000000\times 2.998}}$$

Multiply 3.6 and 10000000000 to get 36000000000.

$$1-\sqrt{1-\frac{79.28712}{36000000000\times 2.998}}$$

Multiply 36000000000 and 2.998 to get 107928000000.

$$1-\sqrt{1-\frac{79.28712}{107928000000}}$$

Expand \frac{79.28712}{107928000000} by multiplying both numerator and the denominator by 100000.

$$1-\sqrt{1-\frac{7928712}{10792800000000000}}$$

Reduce the fraction \frac{7928712}{10792800000000000} to lowest terms by extracting and canceling out 72.

$$1-\sqrt{1-\frac{110121}{149900000000000}}$$

Convert 1 to fraction \frac{149900000000000}{149900000000000}.

$$1-\sqrt{\frac{149900000000000}{149900000000000}-\frac{110121}{149900000000000}}$$

Since \frac{149900000000000}{149900000000000} and \frac{110121}{149900000000000} have the same denominator, subtract them by subtracting their numerators.

$$1-\sqrt{\frac{149900000000000-110121}{149900000000000}}$$

Subtract 110121 from 149900000000000 to get 149899999889879.

$$1-\sqrt{\frac{149899999889879}{149900000000000}}$$

Rewrite the square root of the division \sqrt{\frac{149899999889879}{149900000000000}} as the division of square roots \frac{\sqrt{149899999889879}}{\sqrt{149900000000000}}.

$$1-\frac{\sqrt{149899999889879}}{\sqrt{149900000000000}}$$

Factor 149900000000000=100000^{2}\times 14990. Rewrite the square root of the product \sqrt{100000^{2}\times 14990} as the product of square roots \sqrt{100000^{2}}\sqrt{14990}. Take the square root of 100000^{2}.

$$1-\frac{\sqrt{149899999889879}}{100000\sqrt{14990}}$$

Rationalize the denominator of \frac{\sqrt{149899999889879}}{100000\sqrt{14990}} by multiplying numerator and denominator by \sqrt{14990}.

$$1-\frac{\sqrt{149899999889879}\sqrt{14990}}{100000\left(\sqrt{14990}\right)^{2}}$$

The square of \sqrt{14990} is 14990.

$$1-\frac{\sqrt{149899999889879}\sqrt{14990}}{100000\times 14990}$$

To multiply \sqrt{149899999889879} and \sqrt{14990}, multiply the numbers under the square root.

$$1-\frac{\sqrt{2247000998349286210}}{100000\times 14990}$$

Multiply 100000 and 14990 to get 1499000000.

$$1-\frac{\sqrt{2247000998349286210}}{1499000000}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1499000000}{1499000000}.

$$\frac{1499000000}{1499000000}-\frac{\sqrt{2247000998349286210}}{1499000000}$$

Since \frac{1499000000}{1499000000} and \frac{\sqrt{2247000998349286210}}{1499000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1499000000-\sqrt{2247000998349286210}}{1499000000}$$