The number that multiplies by itself to reach yours
Find the square root of any positive number, with enough decimal places for geometry, construction and physics work.
A square root answers a geometric question: given an area, how long is the side of the square? The area 144 gives a side of 12.
Most roots are irrational — they run forever without repeating. √2 starts 1.41421356 and never settles, which is exactly what unsettled the ancient Greeks about it.
What this calculator shows
- The square root to several decimal places
- Instant identification of perfect squares
- Precision suitable for diagonals, distances and areas
What to keep in mind
- Returns the positive root. Strictly, 9 has roots of both 3 and −3.
- Negative inputs have no real square root; they belong to the imaginary numbers.
FAQs
What is the square root of 144?
12, because 12 × 12 = 144. It is a perfect square, so the answer is a whole number.
Why can't I take the square root of a negative number?
Because any real number times itself is positive. Mathematics gets around it by inventing i, where i² = −1, but that leaves the real number line.
How would I estimate √50 without a calculator?
It sits between √49 = 7 and √64 = 8, much closer to 7. The actual value is 7.07.
What is a perfect square?
A number whose root is a whole number: 1, 4, 9, 16, 25, 36 and so on. Everything between them has an irrational root.
Worked example
The diagonal of a square room
Input: √32
Output: 5.657
Note: A room 4 m by 4 m has a diagonal of √(16+16) = √32, about 5.66 m — worth knowing before carrying a sofa through it.