Solve 0.5*20/500[1-sqrt{1-4.6*7.02*10^4/20*1000*150}]1000*150

$$\frac { 0.5 \times 20 } { 500 } [ 1 - \sqrt { 1 - \frac { 4.6 \times 7.02 \times 10 ^ { 4 } } { 20 \times 1000 \times 150 } } ] 1000 \times 150$$

Evaluate

$$3000-6\sqrt{223090}\approx 166.055752136$$

Short Solution Steps

Multiply 150 and 1000 to get 150000.

$$150000\times \frac{0.5\times 20}{500}\left(1-\sqrt{1-\frac{4.6\times 7.02\times 10^{4}}{20\times 1000\times 150}}\right)$$

Multiply 0.5 and 20 to get 10.

$$150000\times \frac{10}{500}\left(1-\sqrt{1-\frac{4.6\times 7.02\times 10^{4}}{20\times 1000\times 150}}\right)$$

Reduce the fraction \frac{10}{500} to lowest terms by extracting and canceling out 10.

$$150000\times \frac{1}{50}\left(1-\sqrt{1-\frac{4.6\times 7.02\times 10^{4}}{20\times 1000\times 150}}\right)$$

Multiply 150000 and \frac{1}{50} to get \frac{150000}{50}.

$$\frac{150000}{50}\left(1-\sqrt{1-\frac{4.6\times 7.02\times 10^{4}}{20\times 1000\times 150}}\right)$$

Divide 150000 by 50 to get 3000.

$$3000\left(1-\sqrt{1-\frac{4.6\times 7.02\times 10^{4}}{20\times 1000\times 150}}\right)$$

Multiply 4.6 and 7.02 to get 32.292.

$$3000\left(1-\sqrt{1-\frac{32.292\times 10^{4}}{20\times 1000\times 150}}\right)$$

Calculate 10 to the power of 4 and get 10000.

$$3000\left(1-\sqrt{1-\frac{32.292\times 10000}{20\times 1000\times 150}}\right)$$

Multiply 32.292 and 10000 to get 322920.

$$3000\left(1-\sqrt{1-\frac{322920}{20\times 1000\times 150}}\right)$$

Multiply 20 and 1000 to get 20000.

$$3000\left(1-\sqrt{1-\frac{322920}{20000\times 150}}\right)$$

Multiply 20000 and 150 to get 3000000.

$$3000\left(1-\sqrt{1-\frac{322920}{3000000}}\right)$$

Reduce the fraction \frac{322920}{3000000} to lowest terms by extracting and canceling out 120.

$$3000\left(1-\sqrt{1-\frac{2691}{25000}}\right)$$

Convert 1 to fraction \frac{25000}{25000}.

$$3000\left(1-\sqrt{\frac{25000}{25000}-\frac{2691}{25000}}\right)$$

Since \frac{25000}{25000} and \frac{2691}{25000} have the same denominator, subtract them by subtracting their numerators.

$$3000\left(1-\sqrt{\frac{25000-2691}{25000}}\right)$$

Subtract 2691 from 25000 to get 22309.

$$3000\left(1-\sqrt{\frac{22309}{25000}}\right)$$

Rewrite the square root of the division \sqrt{\frac{22309}{25000}} as the division of square roots \frac{\sqrt{22309}}{\sqrt{25000}}.

$$3000\left(1-\frac{\sqrt{22309}}{\sqrt{25000}}\right)$$

Factor 25000=50^{2}\times 10. Rewrite the square root of the product \sqrt{50^{2}\times 10} as the product of square roots \sqrt{50^{2}}\sqrt{10}. Take the square root of 50^{2}.

$$3000\left(1-\frac{\sqrt{22309}}{50\sqrt{10}}\right)$$

Rationalize the denominator of \frac{\sqrt{22309}}{50\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$3000\left(1-\frac{\sqrt{22309}\sqrt{10}}{50\left(\sqrt{10}\right)^{2}}\right)$$

The square of \sqrt{10} is 10.

$$3000\left(1-\frac{\sqrt{22309}\sqrt{10}}{50\times 10}\right)$$

To multiply \sqrt{22309} and \sqrt{10}, multiply the numbers under the square root.

$$3000\left(1-\frac{\sqrt{223090}}{50\times 10}\right)$$

Multiply 50 and 10 to get 500.

$$3000\left(1-\frac{\sqrt{223090}}{500}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{500}{500}.

$$3000\left(\frac{500}{500}-\frac{\sqrt{223090}}{500}\right)$$

Since \frac{500}{500} and \frac{\sqrt{223090}}{500} have the same denominator, subtract them by subtracting their numerators.

$$3000\times \frac{500-\sqrt{223090}}{500}$$

Cancel out 500, the greatest common factor in 3000 and 500.

$$6\left(500-\sqrt{223090}\right)$$

Use the distributive property to multiply 6 by 500-\sqrt{223090}.

$$3000-6\sqrt{223090}$$