Solve 5sqrt{435450/90}-(6040/70)^2

$$5 \sqrt { \frac { 435450 } { 90 } } - ( \frac { 6040 } { 70 } ) ^ { 2 }$$

Evaluate

$$\frac{5\sqrt{43545}}{3}-\frac{364816}{49}\approx -7097.433843957$$

Short Solution Steps

Reduce the fraction \frac{435450}{90} to lowest terms by extracting and canceling out 30.

$$5\sqrt{\frac{14515}{3}}-\left(\frac{6040}{70}\right)^{2}$$

Rewrite the square root of the division \sqrt{\frac{14515}{3}} as the division of square roots \frac{\sqrt{14515}}{\sqrt{3}}.

$$5\times \frac{\sqrt{14515}}{\sqrt{3}}-\left(\frac{6040}{70}\right)^{2}$$

Rationalize the denominator of \frac{\sqrt{14515}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$5\times \frac{\sqrt{14515}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\left(\frac{6040}{70}\right)^{2}$$

The square of \sqrt{3} is 3.

$$5\times \frac{\sqrt{14515}\sqrt{3}}{3}-\left(\frac{6040}{70}\right)^{2}$$

To multiply \sqrt{14515} and \sqrt{3}, multiply the numbers under the square root.

$$5\times \frac{\sqrt{43545}}{3}-\left(\frac{6040}{70}\right)^{2}$$

Express 5\times \frac{\sqrt{43545}}{3} as a single fraction.

$$\frac{5\sqrt{43545}}{3}-\left(\frac{6040}{70}\right)^{2}$$

Reduce the fraction \frac{6040}{70} to lowest terms by extracting and canceling out 10.

$$\frac{5\sqrt{43545}}{3}-\left(\frac{604}{7}\right)^{2}$$

Calculate \frac{604}{7} to the power of 2 and get \frac{364816}{49}.

$$\frac{5\sqrt{43545}}{3}-\frac{364816}{49}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 49 is 147. Multiply \frac{5\sqrt{43545}}{3} times \frac{49}{49}. Multiply \frac{364816}{49} times \frac{3}{3}.

$$\frac{49\times 5\sqrt{43545}}{147}-\frac{364816\times 3}{147}$$

Since \frac{49\times 5\sqrt{43545}}{147} and \frac{364816\times 3}{147} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49\times 5\sqrt{43545}-364816\times 3}{147}$$

Do the multiplications in 49\times 5\sqrt{43545}-364816\times 3.

$$\frac{245\sqrt{43545}-1094448}{147}$$

Factor

$$\frac{245 \sqrt{43545} - 1094448}{147} = -7097.433843956595$$