Solve {left({left(sqrt{73/15}right)}^2right)}^2

$${ \left( { \left( \sqrt{ 7 \frac { 3 } { 15 } } \right) }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$\frac{1296}{25}=51.84$$

Solution Steps

Multiply 7 and 15 to get 105.

$$\left(\left(\sqrt{\frac{105+3}{15}}\right)^{2}\right)^{2}$$

Add 105 and 3 to get 108.

$$\left(\left(\sqrt{\frac{108}{15}}\right)^{2}\right)^{2}$$

Reduce the fraction \frac{108}{15} to lowest terms by extracting and canceling out 3.

$$\left(\left(\sqrt{\frac{36}{5}}\right)^{2}\right)^{2}$$

The square of \sqrt{\frac{36}{5}} is \frac{36}{5}.

$$\left(\frac{36}{5}\right)^{2}$$

Calculate \frac{36}{5} to the power of 2 and get \frac{1296}{25}.

$$\frac{1296}{25}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {4}}{5 ^ {2}} = 51\frac{21}{25} = 51.84$$