Solve 5^2+(5/3)*3^2*(2sqrt{5})^2+(5/4)*3

$$5 ^ { 2 } + ( \frac { 5 } { 3 } ) \cdot 3 ^ { 2 } \cdot ( 2 \sqrt { 5 } ) ^ { 2 } + ( \frac { 5 } { 4 } ) \cdot 3$$

Evaluate

$$\frac{1315}{4}=328.75$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25+\frac{5}{3}\times 3^{2}\times \left(2\sqrt{5}\right)^{2}+\frac{5}{4}\times 3$$

Calculate 3 to the power of 2 and get 9.

$$25+\frac{5}{3}\times 9\times \left(2\sqrt{5}\right)^{2}+\frac{5}{4}\times 3$$

Multiply \frac{5}{3} and 9 to get 15.

$$25+15\times \left(2\sqrt{5}\right)^{2}+\frac{5}{4}\times 3$$

Expand \left(2\sqrt{5}\right)^{2}.

$$25+15\times 2^{2}\left(\sqrt{5}\right)^{2}+\frac{5}{4}\times 3$$

Calculate 2 to the power of 2 and get 4.

$$25+15\times 4\left(\sqrt{5}\right)^{2}+\frac{5}{4}\times 3$$

The square of \sqrt{5} is 5.

$$25+15\times 4\times 5+\frac{5}{4}\times 3$$

Multiply 4 and 5 to get 20.

$$25+15\times 20+\frac{5}{4}\times 3$$

Multiply 15 and 20 to get 300.

$$25+300+\frac{5}{4}\times 3$$

Add 25 and 300 to get 325.

$$325+\frac{5}{4}\times 3$$

Multiply \frac{5}{4} and 3 to get \frac{15}{4}.

$$325+\frac{15}{4}$$

Add 325 and \frac{15}{4} to get \frac{1315}{4}.

$$\frac{1315}{4}$$

Factor

$$\frac{5 \cdot 263}{2 ^ {2}} = 328\frac{3}{4} = 328.75$$