Calculate fourth roots, nth roots, and x⁴ powers from any number, showing decimal and simplified radical results with real roots.
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Fourth Root Formula
- N — the number you want the fourth root of
- ⁴√N — the principal (non-negative) fourth root
The other two modes use related formulas:
For real numbers, N must be ≥ 0 when taking an even root. If N > 0, there are two real fourth roots: +⁴√N and -⁴√N. The calculator returns the principal (positive) value. Even roots of negative numbers are not real and are blocked.
Common Fourth Roots and Perfect Fourth Powers
Use these to sanity-check the calculator or recognize perfect fourth powers on sight.
| N | ⁴√N (decimal) | Simplified |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1.18921 | ⁴√2 |
| 10 | 1.77828 | ⁴√10 |
| 16 | 2 | 2 |
| 32 | 2.37841 | 2⁴√2 |
| 81 | 3 | 3 |
| 256 | 4 | 4 |
| 625 | 5 | 5 |
| 1296 | 6 | 6 |
| 10000 | 10 | 10 |
| Notation | Meaning |
|---|---|
| ⁴√N | Principal fourth root of N |
| N^(1/4) | Same value, written as a power |
| N^0.25 | Decimal exponent form, used in spreadsheets |
| √(√N) | Square root applied twice — equals ⁴√N |
Worked Examples and FAQ
Example 1: Find ⁴√625. Since 5 × 5 × 5 × 5 = 625, the fourth root is 5.
Example 2: Find ⁴√48. Factor: 48 = 16 × 3 = 2⁴ × 3. Pull the 2⁴ out: ⁴√48 = 2⁴√3 ≈ 2.6322.
Example 3: Find ⁴√0.0625. Rewrite as 1/16, so ⁴√(1/16) = 1/2 = 0.5.
Can you take the fourth root of a negative number? Not in the real numbers. (-1)^(1/4) has no real value because any real number raised to the 4th power is non-negative. Complex roots exist but this calculator returns real results only.
Why are there two fourth roots? Both 3⁴ and (-3)⁴ equal 81. Any positive N has a positive and a negative real fourth root. The principal root is the positive one.
How is it different from a square root? ⁴√N = √(√N). Taking the square root twice gives the fourth root.
How do I type it in a spreadsheet? Use =N^(1/4) or =N^0.25.
