Solve {left(999/sqrt{69}right)}^2

$${ \left(9 \frac{ 99 }{ \sqrt{ 69 } } \right) }^{ 2 }$$

Evaluate

$$\frac{264627}{23}\approx 11505.52173913$$

Solution Steps

Rationalize the denominator of \frac{99}{\sqrt{69}} by multiplying numerator and denominator by \sqrt{69}.

$$\left(9\times \frac{99\sqrt{69}}{\left(\sqrt{69}\right)^{2}}\right)^{2}$$

The square of \sqrt{69} is 69.

$$\left(9\times \frac{99\sqrt{69}}{69}\right)^{2}$$

Divide 99\sqrt{69} by 69 to get \frac{33}{23}\sqrt{69}.

$$\left(9\times \frac{33}{23}\sqrt{69}\right)^{2}$$

Multiply 9 and \frac{33}{23} to get \frac{297}{23}.

$$\left(\frac{297}{23}\sqrt{69}\right)^{2}$$

Expand \left(\frac{297}{23}\sqrt{69}\right)^{2}.

$$\left(\frac{297}{23}\right)^{2}\left(\sqrt{69}\right)^{2}$$

Calculate \frac{297}{23} to the power of 2 and get \frac{88209}{529}.

$$\frac{88209}{529}\left(\sqrt{69}\right)^{2}$$

The square of \sqrt{69} is 69.

$$\frac{88209}{529}\times 69$$

Multiply \frac{88209}{529} and 69 to get \frac{264627}{23}.

$$\frac{264627}{23}$$

Factor

$$\frac{3 ^ {7} \cdot 11 ^ {2}}{23} = 11505\frac{12}{23} = 11505.521739130434$$