Quick start
- Enter the radicand, which is the number inside the root.
- Enter a whole-number root index of 2 or higher.
- Use 2 for square root, 3 for cube root, 4 for fourth root, and so on.
- Press Calculate root.
- Read the answer, exponent form, power check, root type, and steps together.
- If a negative number fails, check whether you used an even root index.
Best uses
Use this guide when you need to understand the root answer, not just copy the final number.
- Find square roots and cube roots for math, science, and study problems.
- Calculate nth roots such as fourth roots, fifth roots, and higher whole-number roots.
- Convert root notation into rational exponent form.
- Check whether a negative radicand has a real-number root.
Quick answer
A root asks which number can be raised to a power to get back to the radicand. If the page says root_2(144) = 12, the check is 12^2 = 144.
The Root Calculator is useful because it does more than give the final number. It also shows exponent form and a power check, so you can see why the answer fits.
What the inputs mean
The radicand is the number inside the root. In root_3(125), the radicand is 125.
The root index tells which power you are undoing. Index 2 means square root, index 3 means cube root, index 5 means fifth root, and so on.
Keep the root index as a whole number. This calculator is built for real-number nth roots such as square roots, cube roots, fourth roots, and fifth roots, not decimal-index roots.
How the calculator math works
The calculator rewrites the nth root of x as x^(1/n). That is why the fourth root of 81 can also be read as 81^(1/4).
After it finds the answer, the power check raises the answer back to the root index. For root_5(32), the result is 2, and the check is 2^5 = 32.
This power check is the fastest way to catch a copied answer that looks right but does not actually return the starting number.
Example: square root of 144
Enter 144 as the radicand and 2 as the root index. The calculator returns 12 because 12^2 = 144.
This is an exact square root. The result does not need rounding, and the power check lands exactly back on the original radicand.
Example: cube root of a negative number
Enter -125 as the radicand and 3 as the root index. The result is -5 because (-5)^3 = -125.
Odd roots can keep the negative sign in real-number math. That is why cube roots, fifth roots, and other odd roots can work with negative radicands.
Example: decimal radicands and fifth roots
Decimal radicands are allowed when the result is a real number. For example, root_3(0.008) returns 0.2 because 0.2^3 = 0.008.
Fifth roots work the same way. root_5(32) returns 2 because 2^5 = 32. The index changes the power check, not the basic idea.
Even roots of negative numbers
An even power is never negative in real-number math. Squaring 4 gives 16, and squaring -4 also gives 16.
That is why root_2(-16) has no real-number answer on this page. If you need complex-number answers such as 4i, this simple real-number calculator is not the right mode yet.
Exact answers versus decimal approximations
Some roots land cleanly on whole numbers, like root_2(144) = 12 or root_4(81) = 3. These are exact roots.
Other roots do not land on a neat whole number. root_2(2) is about 1.41421356, so the calculator returns a decimal approximation. Use the power check and your assignment rules to decide how many decimals to keep.
Mistakes and limits to check
Most bad root answers come from a small input mismatch, not from hard math. Check these before copying the result.
- Do not type the exponent where the root index belongs. The root index is the small number on the root sign.
- Use index 2 for square root even when the small 2 is not written in class notes.
- Use an odd index for negative radicands when you need a real-number answer.
- Do not round too early if the root is part of a longer problem.
- Check decimal placement carefully. The cube root of 0.008 is 0.2, not 2.
- Use the power check before trusting a pasted answer.
When another tool fits better
Use the Exponent Calculator when you already know the base and exponent and want to raise a number to a power.
Use the Scientific Calculator when the root is only one part of a longer expression with trig, logs, constants, or several operations.
Worked examples for Root Calculator
12 because 12^2 = 144
-5 because (-5)^3 = -125
3 because 3^4 = 81
2 because 2^5 = 32
0.2 because 0.2^3 = 0.008
No real-number result
FAQ in plain language
What is the fastest way to check a root answer?
Raise the answer to the root index. If the result returns the radicand, the root answer matches the input.
Why does the calculator show exponent form?
Exponent form shows the same root as a rational exponent. The nth root of x is x^(1/n), so it connects root notation with exponent rules.
Can I use this for cube roots of negative numbers?
Yes. Odd roots of negative numbers can have real-number answers. For example, root_3(-125) returns -5.
Why does an even root of a negative number fail?
Even powers do not create negative real numbers. That is why square roots and fourth roots of negative radicands are blocked on this real-number calculator.
Can the radicand be a decimal?
Yes. Decimal radicands work when the root has a real-number answer, such as root_3(0.008) = 0.2.
Can the root index be a decimal?
No. Use a whole-number index of 2 or higher, such as 2, 3, 4, or 5.
When should I avoid relying on this result?
Do not rely on it for complex-number roots, proof-heavy algebra, or official work where your teacher, software, or form requires a specific rounding rule.
Sources
Use these if you want to compare the formula, inputs, or limits with a trusted outside explanation.
Related tools
- Exponent CalculatorCalculate powers, zero and negative exponents, simple fraction exponents, and scientific notation.
- Log CalculatorCalculate logarithms with custom bases, ln, log10, exponent checks, and change-of-base steps.
- Scientific CalculatorA free scientific calculator for trig, inverse trig, logs, roots, powers, constants, and DEG/RAD mode.
Keep exploring
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- Free calculator resourcesStart here when you are not sure which calculator page fits.
Privacy and copying results
Recent answers stay visible only while you work in the current browser tab. They are not sent to a server.
Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.