Solve {left(7/45/2right)}^2sqrt{4/9}

$${ \left( \frac{ 7 }{ 4 } \frac{ 5 }{ 2 } \right) }^{ 2 } \sqrt{ \frac{ 4 }{ 9 } }$$

Evaluate

$$\frac{1225}{96}\approx 12.760416667$$

Solution Steps

Multiply \frac{7}{4} and \frac{5}{2} to get \frac{35}{8}.

$$\left(\frac{35}{8}\right)^{2}\sqrt{\frac{4}{9}}$$

Calculate \frac{35}{8} to the power of 2 and get \frac{1225}{64}.

$$\frac{1225}{64}\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1225}{64}\times \frac{2}{3}$$

Multiply \frac{1225}{64} and \frac{2}{3} to get \frac{1225}{96}.

$$\frac{1225}{96}$$

Factor

$$\frac{5 ^ {2} \cdot 7 ^ {2}}{2 ^ {5} \cdot 3} = 12\frac{73}{96} = 12.760416666666666$$