Solve {left(22122/514sqrt{31}right)}^2

$${ \left(2 \frac{ 2122 }{ 514 \sqrt{ 31 } } \right) }^{ 2 }$$

Evaluate

$$\frac{4502884}{2047519}\approx 2.199190337$$

Solution Steps

Rationalize the denominator of \frac{2122}{514\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$\left(2\times \frac{2122\sqrt{31}}{514\left(\sqrt{31}\right)^{2}}\right)^{2}$$

The square of \sqrt{31} is 31.

$$\left(2\times \frac{2122\sqrt{31}}{514\times 31}\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$\left(2\times \frac{1061\sqrt{31}}{31\times 257}\right)^{2}$$

Multiply 31 and 257 to get 7967.

$$\left(2\times \frac{1061\sqrt{31}}{7967}\right)^{2}$$

Express 2\times \frac{1061\sqrt{31}}{7967} as a single fraction.

$$\left(\frac{2\times 1061\sqrt{31}}{7967}\right)^{2}$$

To raise \frac{2\times 1061\sqrt{31}}{7967} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2\times 1061\sqrt{31}\right)^{2}}{7967^{2}}$$

Multiply 2 and 1061 to get 2122.

$$\frac{\left(2122\sqrt{31}\right)^{2}}{7967^{2}}$$

Expand \left(2122\sqrt{31}\right)^{2}.

$$\frac{2122^{2}\left(\sqrt{31}\right)^{2}}{7967^{2}}$$

Calculate 2122 to the power of 2 and get 4502884.

$$\frac{4502884\left(\sqrt{31}\right)^{2}}{7967^{2}}$$

The square of \sqrt{31} is 31.

$$\frac{4502884\times 31}{7967^{2}}$$

Multiply 4502884 and 31 to get 139589404.

$$\frac{139589404}{7967^{2}}$$

Calculate 7967 to the power of 2 and get 63473089.

$$\frac{139589404}{63473089}$$

Reduce the fraction \frac{139589404}{63473089} to lowest terms by extracting and canceling out 31.

$$\frac{4502884}{2047519}$$

Factor

$$\frac{2 ^ {2} \cdot 1061 ^ {2}}{31 \cdot 257 ^ {2}} = 2\frac{407846}{2047519} = 2.1991903371836843$$