Solve 54/25left(.54right)^2+5762-sqrt{62864776}

$$\frac{ 54 }{ 25 } { \left(.54 \right) }^{ 2 } +5762- \sqrt{ 62864776 }$$

Evaluate

$$5762.629856-62\sqrt{16354}\approx -2166.101190012$$

Solution Steps

Calculate 0.54 to the power of 2 and get 0.2916.

$$\frac{54}{25}\times 0.2916+5762-\sqrt{62864776}$$

Convert decimal number 0.2916 to fraction \frac{2916}{10000}. Reduce the fraction \frac{2916}{10000} to lowest terms by extracting and canceling out 4.

$$\frac{54}{25}\times \frac{729}{2500}+5762-\sqrt{62864776}$$

Multiply \frac{54}{25} times \frac{729}{2500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{54\times 729}{25\times 2500}+5762-\sqrt{62864776}$$

Do the multiplications in the fraction \frac{54\times 729}{25\times 2500}.

$$\frac{39366}{62500}+5762-\sqrt{62864776}$$

Reduce the fraction \frac{39366}{62500} to lowest terms by extracting and canceling out 2.

$$\frac{19683}{31250}+5762-\sqrt{62864776}$$

Convert 5762 to fraction \frac{180062500}{31250}.

$$\frac{19683}{31250}+\frac{180062500}{31250}-\sqrt{62864776}$$

Since \frac{19683}{31250} and \frac{180062500}{31250} have the same denominator, add them by adding their numerators.

$$\frac{19683+180062500}{31250}-\sqrt{62864776}$$

Add 19683 and 180062500 to get 180082183.

$$\frac{180082183}{31250}-\sqrt{62864776}$$

Factor 62864776=62^{2}\times 16354. Rewrite the square root of the product \sqrt{62^{2}\times 16354} as the product of square roots \sqrt{62^{2}}\sqrt{16354}. Take the square root of 62^{2}.

$$\frac{180082183}{31250}-62\sqrt{16354}$$

Factor

$$\frac{180082183 - 1937500 \sqrt{16354}}{31250} = -2166.1011900123444$$