To write a cube root in WeBWorK, use a fractional exponent: type x^(1/3). WeBWorK does not have a dedicated cube root function like cbrt(), so the fractional exponent approach is the standard method.
The Basic Syntax
WeBWorK treats roots as fractional powers. To enter the cube root of any expression, raise it to the power of 1/3 using the caret symbol. The parentheses around 1/3 are essential. Without them, WeBWorK will misread your expression.
- Cube root of x:
x^(1/3) - Cube root of 8:
8^(1/3) - Cube root of a longer expression:
(x+5)^(1/3)
You can also use ** instead of ^ for exponentiation. Both 8^(1/3) and 8**(1/3) mean the same thing to WeBWorK. Most students stick with ^ because it’s faster to type.
Why Parentheses Matter
If you type x^1/3 without parentheses around the fraction, WeBWorK reads it as “x to the first power, divided by 3,” which simplifies to x/3. That is not a cube root. Always wrap the fractional exponent in parentheses: x^(1/3).
The same rule applies when the base is an expression rather than a single variable. For the cube root of (2x + 1), type (2x+1)^(1/3). The outer parentheses group the base, and the inner parentheses group the exponent.
Handling Negative Numbers
Negative bases with fractional exponents can cause problems in WeBWorK. If you need the cube root of negative 2, typing (-2)^(1/3) may produce an error or an unexpected result, because WeBWorK sometimes interprets fractional powers of negative numbers using complex number rules.
The safer approach is to pull the negative sign outside the exponent. Instead of (-2)^(1/3), type -(2^(1/3)). This tells WeBWorK to compute the cube root of 2 and then negate the result, which gives you the real-valued answer you expect.
Other Roots Work the Same Way
WeBWorK has a built-in sqrt() function for square roots, but no equivalent named function for cube roots, fourth roots, or higher. For any root beyond a square root, use the fractional exponent pattern.
- Fourth root of x:
x^(1/4) - Fifth root of x:
x^(1/5) - Square root of x (either works):
sqrt(x)orx^(1/2)
If your problem involves something like the cube root of x squared, you can combine the exponents into a single fraction: x^(2/3). This is equivalent to taking the cube root of x and then squaring it, or squaring x and then taking the cube root. WeBWorK handles both interpretations the same way.