Online Square Root Calculator
Calculate exact square roots, identify perfect squares, and find the simplest radical form for any positive number.
Enter a positive number to evaluate.
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Understanding Radicals
The anatomy of a square root and how to work with them mathematically.
The Radicand
This is the number inside or under the radical symbol (√). It represents the area of a square in geometric terms.
The Radical Symbol
The mathematical sign that means "root of." When no small number (index) sits in the "v" part of the sign, it defaults to a square root (index 2).
The Root (Result)
The number that, when squared (multiplied by itself), gives you the radicand back. Geometrically, this is the side length of the square.
Frequently Asked Questions
What is a square root?
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 × 5 = 25.
What is the difference between principal and negative roots?
Every positive number technically has two square roots: a positive one and a negative one (because a negative times a negative is a positive, e.g., -5 × -5 = 25). The principal root is simply the positive one, which is what the √ symbol usually implies in general arithmetic.
What is a perfect square?
A perfect square is an integer that is the square of another integer. Examples include 1, 4, 9, 16, 25, 36, and so on. Their square roots are always clean whole numbers.
Can you find the square root of a negative number?
Not in the realm of real numbers. Multiplying two identical real numbers (two positives or two negatives) always results in a positive number. Finding the square root of a negative requires "imaginary numbers", denoted by the letter i.
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