Square Root
The value that squares to n.
Formula
Variables
Example
√81 = 9
How it works
The square root of a number n is the non-negative number that, when multiplied by itself, gives n. In other words, it reverses squaring: if x^2 = n, then x = \sqrt{n}. This idea comes from asking “what side length would make this area?” or “what number produces this square when squared?”
When to use it
Use square roots when you need to undo a square in algebra, geometry, or measurement problems. They also appear when finding side lengths from areas, distances from the Pythagorean theorem, and values in science formulas.
Worked example, step by step
Find \sqrt{49}. Step 1: Look for the number that squares to 49. Step 2: 7 × 7 = 49. Step 3: Therefore, \sqrt{49} = 7.
Common mistakes to avoid
- Forgetting that the square root symbol usually means the non-negative root only
- Confusing \sqrt{n} with n^2 instead of the reverse operation
- Assuming every number has an integer square root, when many square roots are decimals
Did You Know?
The square-root symbol √ is a stylised letter r, from the Latin "radix" meaning root.
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