Solve 2^2+(15/4)^2-2*2*15/4*4/5

$$2 ^ { 2 } + ( \frac { 15 } { 4 } ) ^ { 2 } - 2 \times 2 \times \frac { 15 } { 4 } \times \frac { 4 } { 5 }$$

Evaluate

$$\frac{97}{16}=6.0625$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate \frac{15}{4} to the power of 2 and get \frac{225}{16}.

$$4+\frac{225}{16}-2\times 2\times \frac{15}{4}\times \frac{4}{5}$$

Convert 4 to fraction \frac{64}{16}.

$$\frac{64}{16}+\frac{225}{16}-2\times 2\times \frac{15}{4}\times \frac{4}{5}$$

Since \frac{64}{16} and \frac{225}{16} have the same denominator, add them by adding their numerators.

$$\frac{64+225}{16}-2\times 2\times \frac{15}{4}\times \frac{4}{5}$$

Add 64 and 225 to get 289.

$$\frac{289}{16}-2\times 2\times \frac{15}{4}\times \frac{4}{5}$$

Multiply 2 and 2 to get 4.

$$\frac{289}{16}-4\times \frac{15}{4}\times \frac{4}{5}$$

Cancel out 4 and 4.

$$\frac{289}{16}-15\times \frac{4}{5}$$

Express 15\times \frac{4}{5} as a single fraction.

$$\frac{289}{16}-\frac{15\times 4}{5}$$

Multiply 15 and 4 to get 60.

$$\frac{289}{16}-\frac{60}{5}$$

Divide 60 by 5 to get 12.

$$\frac{289}{16}-12$$

Convert 12 to fraction \frac{192}{16}.

$$\frac{289}{16}-\frac{192}{16}$$

Since \frac{289}{16} and \frac{192}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{289-192}{16}$$

Subtract 192 from 289 to get 97.

$$\frac{97}{16}$$

Factor

$$\frac{97}{2 ^ {4}} = 6\frac{1}{16} = 6.0625$$