Solve 1-sqrt{1-2*6674*594/36*10^7*2998*10^3}

$$1 - \sqrt { 1 - \frac { 2 \times 6674 \times 594 } { 36 \times 10 ^ { 7 } \times 2998 \times 10 ^ { 3 } } }$$

Evaluate

$$-\frac{\sqrt{22470009834928621}}{149900000}+1\approx 3.673148785 \cdot 10^{-9}$$

Short Solution Steps

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

$$1-\sqrt{1-\frac{2\times 6674\times 594}{36\times 10^{10}\times 2998}}$$

Cancel out 2\times 2\times 2\times 9 in both numerator and denominator.

$$1-\sqrt{1-\frac{33\times 3337}{1499\times 10^{10}}}$$

Multiply 33 and 3337 to get 110121.

$$1-\sqrt{1-\frac{110121}{1499\times 10^{10}}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$1-\sqrt{1-\frac{110121}{1499\times 10000000000}}$$

Multiply 1499 and 10000000000 to get 14990000000000.

$$1-\sqrt{1-\frac{110121}{14990000000000}}$$

Convert 1 to fraction \frac{14990000000000}{14990000000000}.

$$1-\sqrt{\frac{14990000000000}{14990000000000}-\frac{110121}{14990000000000}}$$

Since \frac{14990000000000}{14990000000000} and \frac{110121}{14990000000000} have the same denominator, subtract them by subtracting their numerators.

$$1-\sqrt{\frac{14990000000000-110121}{14990000000000}}$$

Subtract 110121 from 14990000000000 to get 14989999889879.

$$1-\sqrt{\frac{14989999889879}{14990000000000}}$$

Rewrite the square root of the division \sqrt{\frac{14989999889879}{14990000000000}} as the division of square roots \frac{\sqrt{14989999889879}}{\sqrt{14990000000000}}.

$$1-\frac{\sqrt{14989999889879}}{\sqrt{14990000000000}}$$

Factor 14990000000000=100000^{2}\times 1499. Rewrite the square root of the product \sqrt{100000^{2}\times 1499} as the product of square roots \sqrt{100000^{2}}\sqrt{1499}. Take the square root of 100000^{2}.

$$1-\frac{\sqrt{14989999889879}}{100000\sqrt{1499}}$$

Rationalize the denominator of \frac{\sqrt{14989999889879}}{100000\sqrt{1499}} by multiplying numerator and denominator by \sqrt{1499}.

$$1-\frac{\sqrt{14989999889879}\sqrt{1499}}{100000\left(\sqrt{1499}\right)^{2}}$$

The square of \sqrt{1499} is 1499.

$$1-\frac{\sqrt{14989999889879}\sqrt{1499}}{100000\times 1499}$$

To multiply \sqrt{14989999889879} and \sqrt{1499}, multiply the numbers under the square root.

$$1-\frac{\sqrt{22470009834928621}}{100000\times 1499}$$

Multiply 100000 and 1499 to get 149900000.

$$1-\frac{\sqrt{22470009834928621}}{149900000}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{149900000}{149900000}.

$$\frac{149900000}{149900000}-\frac{\sqrt{22470009834928621}}{149900000}$$

Since \frac{149900000}{149900000} and \frac{\sqrt{22470009834928621}}{149900000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{149900000-\sqrt{22470009834928621}}{149900000}$$