If you have to calculate the fourth root of a number and you don't know how to do it, our online calculator will solve the problem for you automatically. Just type in the number you want to calculate the fourth root of and click the calculate button to get the result.
What is a fourth root?
The fourth root of a number (x) consists of a mathematical operation such that there is a number (y) that when raised to the fourth, that is, multiplied by itself four times, gives us the initial number x as a result.
y4 = x
Do all negative numbers have a fourth root?
As is the case with the square roots, we can't calculate the fourth root of a negative number either. This is due to the rules of the signs and is that any number multiplied by itself an even number of times, will give us as a result a positive number. This can be easily appreciated with the following example.
- 4 x 4 x 4 x 4 x 4 x 4 = 256
- -4 x -4 x -4 x -4 x -4 = 256
Due to the above, we will never be able to calculate the fourth root of a number less than 0 because there is no number that, when raised to the fourth, gives us a negative value. Actually, we could solve the root by using imaginary numbers but that is not the task we are pursuing here.
What is the fourth root of 81?
Let's see a practical example of everything we have learned about this mathematical operation. The rfourth root of number 81 is equal to 3. You can calculate it with our tool or by raising the number to the fourth:
- 3 x 3 x 3 x 3 x 3 x 3 = 81
If you have doubts to calculate the root of any other number, use the calculator and you will get out of doubts immediately.
Other examples of fourth root
Next we are going to see the result given by other typical examples involving the fourth root:
- Fourth root of 4: 1,414
- Fourth root of 5: 1,495
- Fourth root of 2: 1,189
Except in the last case, which is an exact root, in the rest we are left with a result with decimals.
How to calculate the fourth root in Excel
To calculate the fourth root of a number in excelIn the cell where we want the result to appear, we must write the following formula:
You can also use this other method:
Why did we use this function of excel to calculate the fourth root? Basically because the Microsoft spreadsheet program does not have a concrete formula to get the fourth root of a number, so we have to look for an alternative method to get the result.
What we have done is to express the root as a power in order to obtain its value. You know that the root of a number x can be expressed in the form x1/nwhere n is the value of the radicand, which in this case is the number 4.
If you have any doubts, we recommend that you watch the video above to see a practical example. how Excel is used to perform this mathematical operation.
Symbol of the fourth root
The symbol of this radical function consists of a radical (the typical root symbol) but with index 4 as you can see in the image just above these lines.
It is important to put the number 4 above to the left of the radical, otherwise it is a square root and would not be correct.
How to take a fourth root on a calculator
The normal thing on a scientific calculator is to be able to obtain the square root and the cube root by pressing a key designed for these functions, but what if we want to calculating quarter roots?
The most modern models of scientific calculators come with a key represented by x▀. Look it up on your calculator and you will see that the secondary function of that key allows you to calculate the nth root of any number. That is to say, we will be able to calculate fourth roots, the fifth root, …
Therefore, to solve quarter roots with the calculator you have to type the index number (4 in this case), press the SHIFT key and then press the key with x▀. Then you write the number for which you want to calculate its fourth root, close the parenthesis and press equal to get the result.
In short, if you want to calculate the fourth root of 625 with the calculator this is the sequence of keys to press on your calculator:
4 → SHIFT → x▀ → 625 → ) → =
If you have done it right, the calculator will show you that the result is equal to 5.
In the event that you have had any problems calculating quarter rootsLeave us a comment and we will be happy to help you with any problem you may have.