Fifth Roots Calculator
Instantly find the fifth root of any number. This tool handles both positive and negative inputs, providing precise results for your calculations.
Definition:
y = ⁵√x ⇔ y⁵ = x
Also expressed as: x^(1/5)
⁵√32 = 2 (since 2 * 2 * 2 * 2 * 2 = 32) ⁵√(-243) = -3 (since (-3)⁵ = -243) ⁵√100 ≈ 2.5119
What is a fifth root?
The fifth root of a number x is a value y such that y⁵ = x. For example, the fifth root of 32 is 2 because 2 × 2 × 2 × 2 × 2 = 32.
Can you take the fifth root of a negative number?
Yes! Unlike square roots or fourth roots, fifth roots of negative numbers are real and negative. For example, the fifth root of -32 is -2 because (-2)⁵ = -32.
What is the relationship between power and fifth root?
The fifth root is the inverse operation of raising a number to the fifth power. If 2⁵ = 32, then ⁵√32 = 2.
How is the fifth root denoted?
The fifth root is written as ⁵√x or x^(1/5).
🔗 Related Calculators
📐 Formula
Definition:
y = ⁵√x ⇔ y⁵ = x
Also expressed as: x^(1/5)
📝 Example Calculation
⁵√32 = 2 (since 2 * 2 * 2 * 2 * 2 = 32) ⁵√(-243) = -3 (since (-3)⁵ = -243) ⁵√100 ≈ 2.5119
❓ Frequently Asked Questions
What is a fifth root?▼
The fifth root of a number x is a value y such that y⁵ = x. For example, the fifth root of 32 is 2 because 2 × 2 × 2 × 2 × 2 = 32.
Can you take the fifth root of a negative number?▼
Yes! Unlike square roots or fourth roots, fifth roots of negative numbers are real and negative. For example, the fifth root of -32 is -2 because (-2)⁵ = -32.
What is the relationship between power and fifth root?▼
The fifth root is the inverse operation of raising a number to the fifth power. If 2⁵ = 32, then ⁵√32 = 2.
How is the fifth root denoted?▼
The fifth root is written as ⁵√x or x^(1/5).