What Is the Fourth Roots Calculator?
The Fourth Roots Calculator finds the number that, when multiplied by itself four times, equals the value you enter. In symbols, if x is the fourth root of y, then \(x \times x \times x \times x = y\). This is written as \(x = \sqrt[4]{y}\) or equivalently \(x = y^{1/4}\). The tool also shows the square root for comparison, since the fourth root is simply the square root of the square root.
How to Use It
Type any non-negative number into the Number (y) field and the calculator instantly returns its principal (positive) fourth root. For example, the fourth root of 16 is 2, because \(2 \times 2 \times 2 \times 2 = 16\). Note that every positive number actually has two real fourth roots — a positive one and its negative — so \(\pm 2\) are both fourth roots of 16. Negative inputs have no real fourth root.
The Formula Explained
The core formula is $$x = y^{1/4}.$$ Raising a number to the power 1/4 is the inverse of raising it to the power 4. Because the fourth root can be split as \(\sqrt{\sqrt{y}}\), you can also compute it by taking the square root twice. The principal fourth root is always reported as a non-negative value.
Worked Example
Suppose \(y = 81\). The fourth root is \(81^{1/4}\). Since \(3^4 = 81\), the principal fourth root is 3. You can verify with the square-root method: $$\sqrt{81} = 9, \quad \sqrt{9} = 3.$$ The negative root, \(-3\), also satisfies \((-3)^4 = 81\).
FAQ
Can I take the fourth root of a negative number? Not within the real numbers — the result would be complex. This calculator handles non-negative inputs.
How many fourth roots does a positive number have? Two real ones (a positive value and its negative) plus two complex ones. We display the positive principal root.
Is the fourth root the same as the square root twice? Yes. Taking the square root of a number and then the square root again gives its fourth root.
