Solve 5sqrt{435650/90}-{left(6040/90right)}^2

$$5 \sqrt{ \frac{ 435650 }{ 90 } } - { \left( \frac{ 6040 }{ 90 } \right) }^{ 2 }$$

Evaluate

$$\frac{5\sqrt{43565}}{3}-\frac{364816}{81}\approx -4156.030728648$$

Short Solution Steps

Reduce the fraction \frac{435650}{90} to lowest terms by extracting and canceling out 10.

$$5\sqrt{\frac{43565}{9}}-\left(\frac{6040}{90}\right)^{2}$$

Rewrite the square root of the division \sqrt{\frac{43565}{9}} as the division of square roots \frac{\sqrt{43565}}{\sqrt{9}}.

$$5\times \frac{\sqrt{43565}}{\sqrt{9}}-\left(\frac{6040}{90}\right)^{2}$$

Calculate the square root of 9 and get 3.

$$5\times \frac{\sqrt{43565}}{3}-\left(\frac{6040}{90}\right)^{2}$$

Express 5\times \frac{\sqrt{43565}}{3} as a single fraction.

$$\frac{5\sqrt{43565}}{3}-\left(\frac{6040}{90}\right)^{2}$$

Reduce the fraction \frac{6040}{90} to lowest terms by extracting and canceling out 10.

$$\frac{5\sqrt{43565}}{3}-\left(\frac{604}{9}\right)^{2}$$

Calculate \frac{604}{9} to the power of 2 and get \frac{364816}{81}.

$$\frac{5\sqrt{43565}}{3}-\frac{364816}{81}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 81 is 81. Multiply \frac{5\sqrt{43565}}{3} times \frac{27}{27}.

$$\frac{27\times 5\sqrt{43565}}{81}-\frac{364816}{81}$$

Since \frac{27\times 5\sqrt{43565}}{81} and \frac{364816}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27\times 5\sqrt{43565}-364816}{81}$$

Do the multiplications in 27\times 5\sqrt{43565}-364816.

$$\frac{135\sqrt{43565}-364816}{81}$$

Factor

$$\frac{135 \sqrt{43565} - 364816}{81} = -4156.030728648114$$