Cube Root of 405
In this article we will look at the cube root of the number 405 and show you how to calculate it and determine if it is a perfect cube or not.
What is a cube root?
The cube root of 405 is another number that when multiplied by itself twice, would be exactly equal to 405.
We would normally express this problem in mathematical form by using the cube root symbol with the number alongside it:
You might notice that this symbol is very similar to the square root symbol. The only difference is the number, called the index, above the symbol, which lets us know this a cube root calculation.
To recap: the
√ symbol itself is called the radical symbol, the number above it is called the index, and the actual number, 405, is called the radicand.
The basic formula we use to calculate a cube number from the result is a number which we'll call
n in this example, that when multiplied by itself twice, is equal to 405:
When we use
∛405, the actual math calculation we perform is
405⅓. This means you can use that formula in Excel, Google Sheets, or Mac Numbers to calculate the cube root:
We calculated the cubic root of 405 for this article using a scientific calculator. If you have one yourself, you can confirm the results by typing the following into the calculator:
- Type the number: 405
- Press the
You should now be able to confirm that the cube root of 405 is:
Is 405 a perfect cube number?
Whenever the cube root of a given number is a whole number without any fractional or decimal part, we call this a perfect cube.
These are important for a lot of different math functions and can be used in simpler settings like carpenty and room design all the way through to more advanced calculations in physics and astronomy.
For the number 405 we have already calculated the answer of
7.3986362229914 using a scientific calculator and since this is not a whole number, we also know that 405 is not a perfect cube number.
We have a list of perfect cubes article which covers the first 500 perfect cube numbers for you.
Is the cube root of 405 a rational or irrational number?
This is a commonly asked question and the answer to whether the cube root of 405 is rational or irrational is always the same as if it is a perfect cube.
Remember that a rational number can be written as a fraction, while irrational numbers can't.
So, if a number is a perfect cube, then it's a rational number, but if it is not a perfect cube then it is an irrational number.
We just confirmed that 405 is not a rational number then, because we know it is not a perfect cube number.
Rounding the cube root of 405
There might be occasions when you need to round the result of a cube root calculation down to a specific number of decimal places. Below, we show an example of a few of these to specific decimal places that show up in exam questions:
10th: ∛405 = 7.4
100th: ∛405 = 7.40
1000th: ∛405 = 7.399
Simplifying the cube root of 405
Sometimes, the radicand can be simplified and made smaller. If that is possible, we call it the cube root of 405 in its simplest form.
In our example, the cube root of 405 can be simplified and expressed in its simplest form:
Practice perfect cube and cube roots using examples
Still here and interested in perfect cubes? You must really love yourself some math!
Take a look at the random calculations in the sidebar on the right hand side of this page and click through to some of the cube root calculations.
How many of them are perfect cubes? You can also try to think of and calculate some perfect cubes yourself without looking at the list above to test yourself.
Calculate a cube root problem
If you have an example you want to try and see if it is a perfect cube, enter it in the form below and click calculate to find out if it is.
Enter your number in box A below and click "Calculate" to work out the cube root of the given number.