Solve (300-700/sqrt{109})^2

$$( 300 - \frac { 700 } { \sqrt { 109 } } ) ^ { 2 }$$

Evaluate

$$\frac{10300000-420000\sqrt{109}}{109}\approx 54266.708864748$$

Short Solution Steps

Rationalize the denominator of \frac{700}{\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\left(300-\frac{700\sqrt{109}}{\left(\sqrt{109}\right)^{2}}\right)^{2}$$

The square of \sqrt{109} is 109.

$$\left(300-\frac{700\sqrt{109}}{109}\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 300 times \frac{109}{109}.

$$\left(\frac{300\times 109}{109}-\frac{700\sqrt{109}}{109}\right)^{2}$$

Since \frac{300\times 109}{109} and \frac{700\sqrt{109}}{109} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{300\times 109-700\sqrt{109}}{109}\right)^{2}$$

Do the multiplications in 300\times 109-700\sqrt{109}.

$$\left(\frac{32700-700\sqrt{109}}{109}\right)^{2}$$

To raise \frac{32700-700\sqrt{109}}{109} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(32700-700\sqrt{109}\right)^{2}}{109^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(32700-700\sqrt{109}\right)^{2}.

$$\frac{1069290000-45780000\sqrt{109}+490000\left(\sqrt{109}\right)^{2}}{109^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{1069290000-45780000\sqrt{109}+490000\times 109}{109^{2}}$$

Multiply 490000 and 109 to get 53410000.

$$\frac{1069290000-45780000\sqrt{109}[phone]}{109^{2}}$$

Add 1069290000 and 53410000 to get 1122700000.

$$\frac{1122700000-45780000\sqrt{109}}{109^{2}}$$

Calculate 109 to the power of 2 and get 11881.

$$\frac{1122700000-45780000\sqrt{109}}{11881}$$

Expand

$$\frac{10300000 - 420000 \sqrt{109}}{109} = 54266.70886474833$$

Short Solution Steps

Rationalize the denominator of \frac{700}{\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\left(300-\frac{700\sqrt{109}}{\left(\sqrt{109}\right)^{2}}\right)^{2}$$

The square of \sqrt{109} is 109.

$$\left(300-\frac{700\sqrt{109}}{109}\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 300 times \frac{109}{109}.

$$\left(\frac{300\times 109}{109}-\frac{700\sqrt{109}}{109}\right)^{2}$$

Since \frac{300\times 109}{109} and \frac{700\sqrt{109}}{109} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{300\times 109-700\sqrt{109}}{109}\right)^{2}$$

Do the multiplications in 300\times 109-700\sqrt{109}.

$$\left(\frac{32700-700\sqrt{109}}{109}\right)^{2}$$

To raise \frac{32700-700\sqrt{109}}{109} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(32700-700\sqrt{109}\right)^{2}}{109^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(32700-700\sqrt{109}\right)^{2}.

$$\frac{1069290000-45780000\sqrt{109}+490000\left(\sqrt{109}\right)^{2}}{109^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{1069290000-45780000\sqrt{109}+490000\times 109}{109^{2}}$$

Multiply 490000 and 109 to get 53410000.

$$\frac{1069290000-45780000\sqrt{109}[phone]}{109^{2}}$$

Add 1069290000 and 53410000 to get 1122700000.

$$\frac{1122700000-45780000\sqrt{109}}{109^{2}}$$

Calculate 109 to the power of 2 and get 11881.

$$\frac{1122700000-45780000\sqrt{109}}{11881}$$