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.