Solve frac{145sqrt{145^2-4*500}}{2}

$$\frac { 145 \sqrt { 145 ^ { 2 } - 4 \times 500 } } { 2 }$$

Evaluate

$$\frac{725\sqrt{761}}{2}\approx 10000.007812497$$

Solution Steps

Calculate 145 to the power of 2 and get 21025.

$$\frac{145\sqrt{21025-4\times 500}}{2}$$

Multiply 4 and 500 to get 2000.

$$\frac{145\sqrt{21025-2000}}{2}$$

Subtract 2000 from 21025 to get 19025.

$$\frac{145\sqrt{19025}}{2}$$

Factor 19025=5^{2}\times 761. Rewrite the square root of the product \sqrt{5^{2}\times 761} as the product of square roots \sqrt{5^{2}}\sqrt{761}. Take the square root of 5^{2}.

$$\frac{145\times 5\sqrt{761}}{2}$$

Multiply 145 and 5 to get 725.

$$\frac{725\sqrt{761}}{2}$$