How to Calculate Square Root & Powers
What is Square Root & Powers?
Square roots, cube roots, and nth roots are inverses of exponentiation. The square root of n is the number that when multiplied by itself gives n. Roots appear throughout geometry, physics, and statistics.
Formula
Square root: √x = x^(1/2) | Cube root: ∛x = x^(1/3) | General: ⁿ√x = x^(1/n)
- x
- Radicand (Number Under Root) (value)
- n
- Root Degree (integer)
- √x
- Root Result (value)
Step-by-Step Guide
- 1Square root: √n = n^(1/2)
- 2Cube root: ∛n = n^(1/3)
- 3nth root: ⁿ√n = n^(1/n)
- 4For negative numbers, square root is imaginary (i)
Worked Examples
Input
√64
Result
8 (because 8² = 64)
Input
∛27
Result
3 (because 3³ = 27)
Input
√2
Result
1.41421356… (irrational number)
Frequently Asked Questions
What is the difference between a square root and a radical?
A radical is the symbol √. A square root is the most common radical (root degree 2). All roots use the radical symbol but with different degrees.
Can I take the square root of a negative number?
Not in real numbers. Negative square roots require imaginary numbers (using i = √−1). Most calculators only handle real roots.
How do I simplify a square root like √72?
Factor out perfect squares: √72 = √(36×2) = 6√2. This is the simplified form.
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