Write the Java expression for:

$\dfrac{|x - y|}{\sqrt{x} + \sqrt[3]{y}}$

Math.abs(x - y) / (Math.sqrt(x) + Math.cbrt(y))

Reason

• The numerator is $|x - y|$, which in Java is represented by Math.abs(x - y). The Math.abs method computes the absolute value of $x - y$.
• The denominator is $\sqrt{x} + \sqrt[3]{y}$, which in Java is represented by (Math.sqrt(x) + Math.cbrt(y)). Math.sqrt(x) computes the square root of $x$. Math.cbrt(y) computes the cube root of $y$.
• Division (/) has a higher precedence than addition (+). To ensure that the denominator is evaluated correctly as the sum of $\sqrt{x}$ and $\sqrt[3]{y}$, parentheses are used around (Math.sqrt(x) + Math.cbrt(y)). Without parentheses, only Math.sqrt(x) would be divided, leading to incorrect results.
• Math.abs(x - y) ensures the numerator is non-negative. (Math.sqrt(x) + Math.cbrt(y)) ensures the denominator is the sum of the square root of x and the cube root of y, correctly grouped due to the parentheses. The division / then applies to the correctly grouped numerator and denominator.