Square Root Calculator
Free square root calculator: the square root, cube root or any nth root of a number, with the simplified radical form such as √72 = 6√2.
What it does
The square root of a number is the value that multiplied by itself gives that number, and the nth root is the value that multiplied by itself n times gives it. This calculator finds square, cube and any other root, shows the simplified radical when the root is not exact (√72 = 6√2) and checks the result by raising it back to the power.
How to use it
- Type the number.
- Choose square root, cube root or another index.
- See the root, the simplified radical and the check.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
How do I simplify a square root?
Find the largest perfect square that divides the number and take its root out: √72 = √(36 × 2) = 6√2. The calculator does this with the prime factorization.
Can I take the root of a negative number?
Odd roots, yes: ∛−8 = −2, because (−2)³ = −8. Even roots of negative numbers, such as √−4, have no real result; they are the complex numbers 2i and −2i.
Why does a square root have two answers?
Both 5 and −5 squared give 25, but the symbol √ means the positive one (the principal root). When you solve x² = 25, the answer is x = ±5.
What is the relation between roots and exponents?
The nth root is the power 1/n: √x = x^(1/2) and ∛x = x^(1/3). That is why you can also calculate roots with the exponent calculator.
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