Solve sqrt{207600/50}-{left(3180/50right)}^2

$$\sqrt{ \frac{ 207600 }{ 50 } } - { \left( \frac{ 3180 }{ 50 } \right) }^{ 2 }$$

Evaluate

$$2\sqrt{1038}-\frac{101124}{25}\approx -3980.523985226$$

Solution Steps

Divide 207600 by 50 to get 4152.

$$\sqrt{4152}-\left(\frac{3180}{50}\right)^{2}$$

Factor 4152=2^{2}\times 1038. Rewrite the square root of the product \sqrt{2^{2}\times 1038} as the product of square roots \sqrt{2^{2}}\sqrt{1038}. Take the square root of 2^{2}.

$$2\sqrt{1038}-\left(\frac{3180}{50}\right)^{2}$$

Reduce the fraction \frac{3180}{50} to lowest terms by extracting and canceling out 10.

$$2\sqrt{1038}-\left(\frac{318}{5}\right)^{2}$$

Calculate \frac{318}{5} to the power of 2 and get \frac{101124}{25}.

$$2\sqrt{1038}-\frac{101124}{25}$$

Factor

$$\frac{2 {(25 \sqrt{1038} - 50562)}}{25} = -3980.523985225652$$