Solve frac{{left(sqrt{30^2+8^2}right)}^2+30^2-8^2}{2*30*8}

$$\frac{ { \left( \sqrt{ { 30 }^{ 2 } + { 8 }^{ 2 } } \right) }^{ 2 } + { 30 }^{ 2 } - { 8 }^{ 2 } }{ 2 \times 30 \times 8 }$$

Evaluate

$$\frac{15}{4}=3.75$$

Solution Steps

Calculate 30 to the power of 2 and get 900.

$$\frac{\left(\sqrt{900+8^{2}}\right)^{2}+30^{2}-8^{2}}{2\times 30\times 8}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\left(\sqrt{900+64}\right)^{2}+30^{2}-8^{2}}{2\times 30\times 8}$$

Add 900 and 64 to get 964.

$$\frac{\left(\sqrt{964}\right)^{2}+30^{2}-8^{2}}{2\times 30\times 8}$$

The square of \sqrt{964} is 964.

$$\frac{964+30^{2}-8^{2}}{2\times 30\times 8}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{964+900-8^{2}}{2\times 30\times 8}$$

Add 964 and 900 to get 1864.

$$\frac{1864-8^{2}}{2\times 30\times 8}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{1864-64}{2\times 30\times 8}$$

Subtract 64 from 1864 to get 1800.

$$\frac{1800}{2\times 30\times 8}$$

Multiply 2 and 30 to get 60.

$$\frac{1800}{60\times 8}$$

Multiply 60 and 8 to get 480.

$$\frac{1800}{480}$$

Reduce the fraction \frac{1800}{480} to lowest terms by extracting and canceling out 120.

$$\frac{15}{4}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2}} = 3\frac{3}{4} = 3.75$$