What Is the Fifth Roots Calculator?
The Fifth Roots Calculator finds the fifth root of any number you enter. The fifth root of a value y is the number x that, when multiplied by itself five times, produces y (that is, \(x^5 = y\)). It is the inverse operation of raising a number to the fifth power. Because 5 is an odd exponent, every real number — positive, negative, or zero — has exactly one real fifth root, so this tool works for negative inputs too.
How to Use It
Type the number you want the fifth root of into the input field and submit. The calculator returns \(x = y^{1/5}\) along with a verification row reminding you that \(x^5\) equals your original input. Decimals and negative numbers are fully supported.
The Formula Explained
The fifth root is written as $$x = \sqrt[5]{y} = y^{1/5}.$$ Using a fractional exponent of one-fifth is mathematically identical to taking the fifth root. For negative numbers the calculator computes the root of the absolute value and reapplies the negative sign, giving the correct real result: $$\sqrt[5]{-y} = -\sqrt[5]{y}.$$
Worked Example
Suppose \(y = 32\). We look for the number that multiplied by itself five times gives 32. Since $$2 \times 2 \times 2 \times 2 \times 2 = 32,$$ the fifth root of 32 is 2. The calculator returns \(x = 2\). For a negative example, \(\sqrt[5]{-243} = -3\) because \((-3)^5 = -243\).
FAQ
Can I take the fifth root of a negative number? Yes. Unlike even roots, odd roots of negatives are real numbers, so \(\sqrt[5]{-32} = -2\).
Is the fifth root the same as raising to the power 0.2? Yes — \(y^{1/5}\) is the same as \(y^{0.2}\).
What is the fifth root of 0 or 1? The fifth root of 0 is 0, and the fifth root of 1 is 1.
