What is a perfect square?

A perfect square is an integer whose square root is also an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Can you take the square root of a negative number?

Not in the real number system. The square root of a negative number is imaginary (uses the complex unit i). This calculator works with real numbers only.

What is the difference between a root and an exponent?

They are inverse operations. Taking the nth root of x is the same as raising x to the power 1/n. For example, √9 = 9^(1/2) = 3.

What is an irrational root?

Most roots are irrational — they cannot be expressed as a simple fraction. For example, √2 ≈ 1.41421356… continues infinitely without repeating.

How is the cube root different from the square root?

The square root finds a number that when squared gives the original. The cube root finds a number that when cubed gives the original. Cube roots of negative numbers are real (e.g., ∛(−8) = −2).

Math

↵ to calculate

Root Calculator - Square Root Cube Root Online Tool

Calculate square roots, cube roots, and nth roots of any number. Shows decimal result and identifies perfect powers.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The root calculator computes square roots, cube roots, and nth roots of any number. It also identifies whether the result is a perfect power and displays simplified exact forms when applicable.

Number

Root Type

What is Root Calculator - Square Root Cube Root Online Tool?

The root calculator computes square roots, cube roots, and nth roots of any number. It also identifies whether the result is a perfect power and displays simplified exact forms when applicable.

How to use it

1️⃣ Enter the number you want to find the root of.
2️⃣ Select the root type: square root (2nd), cube root (3rd), or nth root.
3️⃣ If you selected nth root, enter the degree (e.g. 4 for a 4th root).
4️⃣ Click Calculate to see the result.
5️⃣ The calculator shows decimal result and whether the input is a perfect power.

Formula

nth root of x = x^(1/n). Square root: x^(1/2) = √x. Cube root: x^(1/3) = ∛x. A number is a perfect nth power if the result is an integer.

💡 See it in action — a real example

Square root of 144 = 12 (perfect square). Cube root of 27 = 3 (perfect cube). 4th root of 256 = 4 (perfect 4th power). Square root of 2 ≈ 1.41421356.

❓ Common questions

What is a perfect square?: A perfect square is an integer whose square root is also an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Can you take the square root of a negative number?: Not in the real number system. The square root of a negative number is imaginary (uses the complex unit i). This calculator works with real numbers only.
What is the difference between a root and an exponent?: They are inverse operations. Taking the nth root of x is the same as raising x to the power 1/n. For example, √9 = 9^(1/2) = 3.
What is an irrational root?: Most roots are irrational — they cannot be expressed as a simple fraction. For example, √2 ≈ 1.41421356… continues infinitely without repeating.
How is the cube root different from the square root?: The square root finds a number that when squared gives the original. The cube root finds a number that when cubed gives the original. Cube roots of negative numbers are real (e.g., ∛(−8) = −2).

⚡ Related Math Tools & Calculators

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