Solve 80-sqrt{80^2-2*2.944*10^6/14.3*1000}

$$80- \sqrt{ { 80 }^{ 2 } - \frac{ 2 \times 2.944 \times { 10 }^{ 6 } }{ 14.3 \times 1000 } }$$

Evaluate

$$-\frac{16\sqrt{478335}}{143}+80\approx 2.616204873$$

Short Solution Steps

Calculate 80 to the power of 2 and get 6400.

$$80-\sqrt{6400-\frac{2\times 2.944\times 10^{6}}{14.3\times 1000}}$$

Cancel out 2 in both numerator and denominator.

$$80-\sqrt{6400-\frac{2.944\times 10^{6}}{14.3\times 500}}$$

Calculate 10 to the power of 6 and get 1000000.

$$80-\sqrt{6400-\frac{2.944\times 1000000}{14.3\times 500}}$$

Multiply 2.944 and 1000000 to get 2944000.

$$80-\sqrt{6400-\frac{2944000}{14.3\times 500}}$$

Multiply 14.3 and 500 to get 7150.

$$80-\sqrt{6400-\frac{2944000}{7150}}$$

Reduce the fraction \frac{2944000}{7150} to lowest terms by extracting and canceling out 50.

$$80-\sqrt{6400-\frac{58880}{143}}$$

Convert 6400 to fraction \frac{915200}{143}.

$$80-\sqrt{\frac{915200}{143}-\frac{58880}{143}}$$

Since \frac{915200}{143} and \frac{58880}{143} have the same denominator, subtract them by subtracting their numerators.

$$80-\sqrt{\frac{915200-58880}{143}}$$

Subtract 58880 from 915200 to get 856320.

$$80-\sqrt{\frac{856320}{143}}$$

Rewrite the square root of the division \sqrt{\frac{856320}{143}} as the division of square roots \frac{\sqrt{856320}}{\sqrt{143}}.

$$80-\frac{\sqrt{856320}}{\sqrt{143}}$$

Factor 856320=16^{2}\times 3345. Rewrite the square root of the product \sqrt{16^{2}\times 3345} as the product of square roots \sqrt{16^{2}}\sqrt{3345}. Take the square root of 16^{2}.

$$80-\frac{16\sqrt{3345}}{\sqrt{143}}$$

Rationalize the denominator of \frac{16\sqrt{3345}}{\sqrt{143}} by multiplying numerator and denominator by \sqrt{143}.

$$80-\frac{16\sqrt{3345}\sqrt{143}}{\left(\sqrt{143}\right)^{2}}$$

The square of \sqrt{143} is 143.

$$80-\frac{16\sqrt{3345}\sqrt{143}}{143}$$

To multiply \sqrt{3345} and \sqrt{143}, multiply the numbers under the square root.

$$80-\frac{16\sqrt{478335}}{143}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 80 times \frac{143}{143}.

$$\frac{80\times 143}{143}-\frac{16\sqrt{478335}}{143}$$

Since \frac{80\times 143}{143} and \frac{16\sqrt{478335}}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{80\times 143-16\sqrt{478335}}{143}$$

Do the multiplications in 80\times 143-16\sqrt{478335}.

$$\frac{11440-16\sqrt{478335}}{143}$$

Factor

$$\frac{16 {(715 - \sqrt{478335})}}{143} = 2.61620487303722$$