Math calculators

Root Calculator

Updated Jul 20, 2026 By Jehan Wadia
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Applies to all three calculators.

Square Root Calculator

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Number Line

Cube Root Calculator

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Number Line

Nth Root Calculator

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Examples:

Number Line


Introduction

This free root calculator lets you find the square root, cube root, or any nth root of a number. Just type in a number, and the tool gives you an answer right away. You can pick how many decimal places you want, see step-by-step work, and view your result on a number line.

A root is the opposite of a power. For example, the square root of 9 is 3 because 3 × 3 = 9. The cube root of 8 is 2 because 2 × 2 × 2 = 8. The nth root works the same way but for any power you choose. This calculator handles all three types so you can solve root problems fast and with no guesswork.

Whether you are a student doing homework, a teacher checking answers, or someone who just needs a quick root value, this tool is built to help. It works with whole numbers, decimals, and even negative numbers when a real root exists.

How to Use Our Root Calculator

Enter a number into any of the three calculators below to find its square root, cube root, or nth root. The tool will show you the answer, the math steps, and a number line.

Decimal Places: Use the dropdown at the top to pick how many decimal places you want in your answer. This setting applies to all three calculators at once.

Square Root Calculator

Number (x): Type the number you want to find the square root of. It must be zero or a positive number. The calculator will return both the positive and negative square roots.

Cube Root Calculator

Number (x): Type any number, including negative numbers. The calculator will find the cube root, which is the number that when multiplied by itself three times equals your input.

Nth Root Calculator

Root Degree (n): Type the root you want to find. This must be a whole number that is 2 or greater. For example, enter 4 to find a fourth root or 5 to find a fifth root.

Number (x): Type the number you want to take the nth root of. If your root degree is even, this number must be zero or positive.

Press the Calculate button or hit Enter to see your result. Use Show Steps to see how the answer was found, and click Copy Result to copy the answer to your clipboard.

What Is a Root in Math?

A root is the opposite of raising a number to a power. When you square a number, you multiply it by itself. For example, 3 × 3 = 9. The square root goes backward — it asks, "What number times itself gives me 9?" The answer is 3.

A cube root works the same way but with three equal factors. Since 2 × 2 × 2 = 8, the cube root of 8 is 2. Cube roots can also handle negative numbers. For example, the cube root of −27 is −3, because −3 × −3 × −3 = −27.

An nth root lets you pick any root degree you want — 4th root, 5th root, 10th root, and so on. The 4th root of 81 is 3, because 3 × 3 × 3 × 3 = 81. The higher the root degree, the closer the result gets to 1 for most numbers.

Even Roots vs. Odd Roots

There is one important rule to know. Even roots (like square roots and 4th roots) only work with zero or positive numbers. You cannot take the square root of a negative number and get a real answer. Even roots also give two answers — one positive and one negative. For instance, both 5 and −5 squared equal 25, so the square root of 25 is ±5.

Odd roots (like cube roots and 5th roots) work with any number, including negatives. They always give exactly one real answer.

How Roots Are Written

Roots use the radical symbol (√). A small number in front of the symbol shows the degree. If there is no small number, it means a square root. A root can also be written as an exponent: the nth root of x is the same as x raised to the power of 1/n. So the cube root of 8 is 81/3, which equals 2. If you need to work with logarithms, roots and logs are closely related since both involve reversing exponential operations.


Formulas used

Square Root
\sqrt{x} = x^{\frac{1}{2}}
Cube Root
\sqrt[3]{x} = x^{\frac{1}{3}}
Nth Root
\sqrt[n]{x} = x^{\frac{1}{n}}
Even-Degree Root of Positive Number
\sqrt[n]{x} = \pm\, |x|^{\frac{1}{n}}, \quad n \text{ even},\; x > 0
Odd-Degree Root of Negative Number
\sqrt[n]{x} = -|x|^{\frac{1}{n}}, \quad n \text{ odd},\; x < 0

Frequently asked questions

What is the difference between a square root and a cube root?

A square root finds a number that, when multiplied by itself two times, gives you the original number. A cube root finds a number that, when multiplied by itself three times, gives you the original number. For example, the square root of 25 is 5 because 5 × 5 = 25, while the cube root of 125 is 5 because 5 × 5 × 5 = 125.

Can I find the square root of a negative number?

No, not with real numbers. A negative number has no real square root because any number multiplied by itself always gives a positive result (or zero). This calculator works with real numbers only. If you enter a negative number in the square root calculator, it will tell you the result is not a real number.

Why does the square root calculator show a ± symbol in the answer?

The ± symbol means "plus or minus." For any positive number, there are two square roots — one positive and one negative. For example, both 4 and −4 squared equal 16, so √16 = ±4. The calculator shows both roots because both are correct answers.

How do I change the number of decimal places in the result?

Use the Decimal Places dropdown at the top of the calculator. You can choose 0, 2, 4, 6, 8, or 10 decimal places. This setting applies to all three calculators — square root, cube root, and nth root — at the same time.

What does root degree mean in the nth root calculator?

The root degree is the "n" in nth root. It tells the calculator which root to find. A root degree of 2 is a square root, 3 is a cube root, 4 is a fourth root, and so on. You must enter a whole number that is 2 or greater.

Why can't I take an even root of a negative number?

Even roots (like 2nd, 4th, or 6th roots) of negative numbers do not exist in real numbers. When you raise any real number to an even power, the result is always zero or positive. So there is no real number that gives a negative result when raised to an even power.

Why can I take a cube root of a negative number but not a square root?

Cube roots are odd roots. When you raise a negative number to an odd power, the result stays negative. For example, (−3) × (−3) × (−3) = −27, so the cube root of −27 is −3. Square roots are even roots, and even powers always give a positive result, so negative numbers have no real square root.

How do I see the step-by-step solution?

Click the Show Steps button below any calculator section. A panel will open showing each step the calculator used to find the answer. Click the button again to hide the steps.

What does the number line show?

The number line is a visual diagram that plots the root value on a line. It helps you see where the result falls relative to zero and other numbers. For even roots, it shows both the positive and negative roots. For odd roots, it shows the single real root.

How do I copy the result to use somewhere else?

Click the Copy Result button next to any calculator. The answer will be copied to your clipboard. You can then paste it into a document, spreadsheet, or any other app.

Is the nth root the same as raising a number to a fraction?

Yes. The nth root of x is the same as x raised to the power of 1/n. For example, the 4th root of 81 is the same as 811/4, which equals 3. This is how the calculator computes roots internally.

What is the square root of zero?

The square root of zero is 0. Zero is the only number whose square root is itself. This applies to cube roots and all nth roots as well — the nth root of 0 is always 0.

Can I use decimals as input?

Yes. You can enter decimals like 0.25, 2.5, or 100.75 into any of the three calculators. The tool handles decimal inputs just like whole numbers.

What is the largest number I can enter?

The calculator works with any number that your browser can handle as a standard JavaScript number. In practice, this means numbers up to about 10308. For everyday math, you will not hit this limit.

Do the example buttons change the calculator settings?

The example buttons only fill in the input fields and run the calculation. They do not change your decimal places setting. You can click any example chip to quickly see a common root problem solved.

What happens if I enter a letter or leave the field blank?

The calculator will show an error message asking you to enter a valid number. It will not produce a result until you type a proper number into the input field.