Comprehensive Calculator Guide
This calculator finds any root of a number, fourth, fifth or higher, as a decimal and in simplest radical form. The fourth root of 81 is 3, the fifth root of 32 is 2, and the fourth root of 48 simplifies to 2∜3. It explains the link with fractional powers and when negatives have roots.
Roots as powers
The nth root of x equals x^(1/n). Even roots of negatives don’t exist in the reals; odd roots keep the sign. Simplify by taking out the largest nth power: ∜48 = ∜(16 × 3) = 2∜3.
How to Use
- Enter the number.
- Enter the index, from 2 to 20.
- Press “Calculate” to see the root as a decimal and in simplest form.
Formula Used
ⁿ√x = x^(1/n) | ⁿ√(aⁿ × b) = a × ⁿ√b
Practical Examples
- Example 1
- Fourth root of 81: 3.
- Example 2
- Fifth root of 32: 2.
- Example 3
- Fourth root of 48: 2∜3, about 2.6321.
Important Tips
- Use the power key: x^(1/n).
- Check by raising the answer to n.
- Watch even indexes with negatives.
Common Mistakes to Avoid
- Raising to n instead of 1/n.
- Taking even roots of negatives.
- Mixing up the index.
Frequently Asked Questions
- How do I find a fourth root?
- Raise to 0.25, or take the square root twice.
- How are roots and powers related?
- ⁿ√x = x^(1/n).
- Do negatives have fifth roots?
- Yes, negative ones.