About Cube Root Calculator
This cube root calculator finds the number that multiplied by itself three times gives your number, and writes it in simplest radical form as well as a decimal. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on the cube root of 40. Since 40 = 2³ × 5, one 2 comes out of the root and the exact form is 2∛5, about 3.41995189. For a perfect cube such as 27 or 343, the answer is a whole number.
Unlike square roots, cube roots of negative numbers are real: the cube root of -27 is -3, because (-3)³ = -27. The calculator keeps the sign and shows the result without any imaginary part.
How to use Cube Root Calculator
- Choose Square root, Cube root, nth root or Simplify radical.
- Type the number. A whole number, a decimal or a fraction all work, and negatives are allowed.
- For an nth root, type the root index. Choose how many decimal places you want.
- Read the exact form and the decimal at the top.
- Open the steps to see the prime factorization and the pairs taken out of the root.
Features
- Simplified radical form with the prime factorization shown: √72 = 6√2.
- Decimal to up to 100 places, computed exactly with integers.
- Square roots, cube roots and nth roots up to index 100.
- Imaginary results for negative numbers under even roots, and real roots for odd ones.
- Perfect squares and perfect powers are recognised and shown exactly.
- Decimals and fractions accepted, with the denominator rationalised.
- Step-by-step working in KaTeX and a copy button.
Simplifying a cube root
A prime must appear three times to leave the root.
∛40 = ∛(2³ × 5) = 2∛5
∛(-x) = -∛xWorked examples
∛40 gives 2∛5 ≈ 3.41995189
40 = 2³ × 5.
∛-27 gives -3
An odd root keeps the sign.
∛2 gives ≈ 1.259921049895
2 is not a perfect cube, so the decimal never ends or repeats.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- To estimate a square root by hand, find the two perfect squares around it. √50 is between √49 = 7 and √64 = 8, so it is a little over 7.
- A decimal that neither ends nor repeats means the root is irrational, which is true of the root of any number that is not a perfect power.
- Check a decimal root by squaring it. The result should be very close to the number you started with.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
Can you take the cube root of a negative number?
Yes. A negative number cubed is negative, so the cube root of -8 is -2.
What are the first perfect cubes?
1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000, which are the cubes of 1 to 10.
More Square Root Calculator pages
- Square Root CalculatorEnter a number to get its square root in simplest radical form and as a decimal, with the working.
- Nth Root CalculatorEnter a number and a root index to get the nth root with the working.
- Simplify Radical CalculatorEnter the number under the root and get the radical in simplest form with the steps.
- Square Root of 2The square root of 2 is about 1.41421356, and its digits never end or repeat.
- Square Root of 3The square root of 3 is about 1.7320508, and its digits never end or repeat.
- Square Root of 72The square root of 72 simplifies to 6√2, which is about 8.4853.