Solve (97/42)^2+(frac{15sqrt{3}}{4})^2

$$( \frac { 97 } { 42 } ) ^ { 2 } + ( \frac { 15 \sqrt { 3 } } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{335311}{7056}\approx 47.521400227$$

Solution Steps

Calculate \frac{97}{42} to the power of 2 and get \frac{9409}{1764}.

$$\frac{9409}{1764}+\left(\frac{15\sqrt{3}}{4}\right)^{2}$$

To raise \frac{15\sqrt{3}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{9409}{1764}+\frac{\left(15\sqrt{3}\right)^{2}}{4^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1764 and 4^{2} is 7056. Multiply \frac{9409}{1764} times \frac{4}{4}. Multiply \frac{\left(15\sqrt{3}\right)^{2}}{4^{2}} times \frac{441}{441}.

$$\frac{9409\times 4}{7056}+\frac{441\times \left(15\sqrt{3}\right)^{2}}{7056}$$

Since \frac{9409\times 4}{7056} and \frac{441\times \left(15\sqrt{3}\right)^{2}}{7056} have the same denominator, add them by adding their numerators.

$$\frac{9409\times 4+441\times \left(15\sqrt{3}\right)^{2}}{7056}$$

Expand \left(15\sqrt{3}\right)^{2}.

$$\frac{9409}{1764}+\frac{15^{2}\left(\sqrt{3}\right)^{2}}{4^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{9409}{1764}+\frac{225\left(\sqrt{3}\right)^{2}}{4^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{9409}{1764}+\frac{225\times 3}{4^{2}}$$

Multiply 225 and 3 to get 675.

$$\frac{9409}{1764}+\frac{675}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9409}{1764}+\frac{675}{16}$$

Add \frac{9409}{1764} and \frac{675}{16} to get \frac{335311}{7056}.

$$\frac{335311}{7056}$$

Factor

$$\frac{547 \cdot 613}{2 ^ {4} \cdot 3 ^ {2} \cdot 7 ^ {2}} = 47\frac{3679}{7056} = 47.52140022675737$$