Solve 489/2+sqrt{{left(489/2right)}^2-29890}

$$\frac{ 489 }{ 2 } + \sqrt{ { \left( \frac{ 489 }{ 2 } \right) }^{ 2 } -29890 }$$

Evaluate

$$\frac{\sqrt{119561}+489}{2}\approx 417.387969506$$

Solution Steps

Calculate \frac{489}{2} to the power of 2 and get \frac{239121}{4}.

$$\frac{489}{2}+\sqrt{\frac{239121}{4}-29890}$$

Convert 29890 to fraction \frac{119560}{4}.

$$\frac{489}{2}+\sqrt{\frac{239121}{4}-\frac{119560}{4}}$$

Since \frac{239121}{4} and \frac{119560}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{489}{2}+\sqrt{\frac{239121-119560}{4}}$$

Subtract 119560 from 239121 to get 119561.

$$\frac{489}{2}+\sqrt{\frac{119561}{4}}$$

Rewrite the square root of the division \sqrt{\frac{119561}{4}} as the division of square roots \frac{\sqrt{119561}}{\sqrt{4}}.

$$\frac{489}{2}+\frac{\sqrt{119561}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{489}{2}+\frac{\sqrt{119561}}{2}$$

Since \frac{489}{2} and \frac{\sqrt{119561}}{2} have the same denominator, add them by adding their numerators.

$$\frac{489+\sqrt{119561}}{2}$$

Factor

$$\frac{\sqrt{119561} + 489}{2} = 417.38796950626727$$