Solve (frac{400sqrt{6}-600}{9})^2+10000

$$( \frac { 400 \sqrt { 6 } - 600 } { 9 } ) ^ { 2 } + 10000$$

Evaluate

$$\frac{710000-160000\sqrt{6}}{27}\approx 11780.801524248$$

Short Solution Steps

To raise \frac{400\sqrt{6}-600}{9} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}}+10000$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10000 times \frac{9^{2}}{9^{2}}.

$$\frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}}+\frac{10000\times 9^{2}}{9^{2}}$$

Since \frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}} and \frac{10000\times 9^{2}}{9^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(400\sqrt{6}-600\right)^{2}+10000\times 9^{2}}{9^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(400\sqrt{6}-600\right)^{2}.

$$\frac{160000\left(\sqrt{6}\right)^{2}-480000\sqrt{6}+360000}{9^{2}}+10000$$

The square of \sqrt{6} is 6.

$$\frac{160000\times 6-480000\sqrt{6}+360000}{9^{2}}+10000$$

Multiply 160000 and 6 to get 960000.

$$\frac{960000-480000\sqrt{6}+360000}{9^{2}}+10000$$

Add 960000 and 360000 to get 1320000.

$$\frac{1320000-480000\sqrt{6}}{9^{2}}+10000$$

Calculate 9 to the power of 2 and get 81.

$$\frac{1320000-480000\sqrt{6}}{81}+10000$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10000 times \frac{81}{81}.

$$\frac{1320000-480000\sqrt{6}}{81}+\frac{10000\times 81}{81}$$

Since \frac{1320000-480000\sqrt{6}}{81} and \frac{10000\times 81}{81} have the same denominator, add them by adding their numerators.

$$\frac{1320000-480000\sqrt{6}+10000\times 81}{81}$$

Do the multiplications in 1320000-480000\sqrt{6}+10000\times 81.

$$\frac{1320000-480000\sqrt{6}+810000}{81}$$

Do the calculations in 1320000-480000\sqrt{6}+810000.

$$\frac{2130000-480000\sqrt{6}}{81}$$

Expand

$$\frac{710000 - 160000 \sqrt{6}}{27} = 11780.801524247834$$

Short Solution Steps

To raise \frac{400\sqrt{6}-600}{9} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}}+10000$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10000 times \frac{9^{2}}{9^{2}}.

$$\frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}}+\frac{10000\times 9^{2}}{9^{2}}$$

Since \frac{\left(400\sqrt{6}-600\right)^{2}}{9^{2}} and \frac{10000\times 9^{2}}{9^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(400\sqrt{6}-600\right)^{2}+10000\times 9^{2}}{9^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(400\sqrt{6}-600\right)^{2}.

$$\frac{160000\left(\sqrt{6}\right)^{2}-480000\sqrt{6}+360000}{9^{2}}+10000$$

The square of \sqrt{6} is 6.

$$\frac{160000\times 6-480000\sqrt{6}+360000}{9^{2}}+10000$$

Multiply 160000 and 6 to get 960000.

$$\frac{960000-480000\sqrt{6}+360000}{9^{2}}+10000$$

Add 960000 and 360000 to get 1320000.

$$\frac{1320000-480000\sqrt{6}}{9^{2}}+10000$$

Calculate 9 to the power of 2 and get 81.

$$\frac{1320000-480000\sqrt{6}}{81}+10000$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10000 times \frac{81}{81}.

$$\frac{1320000-480000\sqrt{6}}{81}+\frac{10000\times 81}{81}$$

Since \frac{1320000-480000\sqrt{6}}{81} and \frac{10000\times 81}{81} have the same denominator, add them by adding their numerators.

$$\frac{1320000-480000\sqrt{6}+10000\times 81}{81}$$

Do the multiplications in 1320000-480000\sqrt{6}+10000\times 81.

$$\frac{1320000-480000\sqrt{6}+810000}{81}$$

Do the calculations in 1320000-480000\sqrt{6}+810000.

$$\frac{2130000-480000\sqrt{6}}{81}$$