How to use
- Type a number, negative numbers allowed.
- Read ∛n as a decimal and in exact simplified form.
- Follow the steps or print the worksheet for practice.
Worked example: ∛(−54)
54 = 2 × 3 × 3 × 3 = 2 × 3³. A group of three 3s leaves the radical as 3; the 2 stays inside. ∛54 = 3∛2 ≈ 3.7798.
The input was negative and cube roots keep the sign, so ∛(−54) = −3∛2 ≈ −3.7798. Check: (−3.7798)³ ≈ −54.
Frequently asked questions
Can I take the cube root of a negative number?
Yes. Odd roots of negatives are real: ∛(−8) = −2 because (−2)³ = −8.
Which numbers are perfect cubes?
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000: cubes of whole numbers.
How is a cube root simplified?
Factor into primes and pull out each group of three as one factor. ∛250 = ∛(125 × 2) = 5∛2.
How accurate is it?
The decimal uses the exact cube-root function, correct to machine precision, displayed at the precision you choose.
What is the cube root of 2?
About 1.2599. It is irrational, so the decimal never ends.
Is there a worksheet?
Yes, twenty problems mixing perfect cubes and non-perfect cubes, with answers.