Example 1
- Number: 81
9
9² = 81 - exact result.
Square root calculator
Type a non-negative number. The square root √x is y ≥ 0 such that y² = x. √81 = 9. √2 is irrational, about 1.41421356 on the page. √0 = 0.
The square root of a negative number does not exist in the real numbers. Zero gives zero: √0 = 0.
Result
Enter a non-negative number.
How does it work?
The square root √x is a number y ≥ 0 such that y² = x. √81 = 9, because 9 × 9 = 81. √0 = 0. Perfect squares 1, 4, 9, 16, 25 give exact results. For √2 and √5 the result is a decimal.
A negative number has no square root in the reals. √(−9) does not run here. 81 to the power 1/2 is the same 9, but this calculator has one Number field. 9² = 81 on the power page runs the other way.
Type 81 in Number and click Calculate. A comma and a period both parse, so 6.25 gives 2.5, because 2.5 × 2.5 = 6.25. Check the note: squaring the result returns the input on a perfect square.
The 3-4-5 triangle uses the same root: √(9+16) = 5, on Pythagoras. Vector length (3, 4) is 5 too. Here you keep one x, not a sum of squares.
Without a number, nothing computes. Typed 0 gives 0. A minus is rejected. The header units do not change 81.
√16 = 4, √100 = 10, √2 ≈ 1.41421356, √5 ≈ 2.23606798. √49 = 7, √121 = 11.
Formula
√x = y when y² = x and y ≥ 0
How to use
- Type a non-negative number in Number, for example 81.
- Click Calculate. √81 = 9. √2 shows about 1.41421356.
- Check that the result squared returns the input. 9 × 9 = 81.
- A negative number does not run in the reals. Typed 0 gives 0.
- √(3²+4²) = 5 lives on Pythagoras or vector length. This page has one field.
√81 = 9 in this calculator
The square root √x is y ≥ 0 such that y² = x. √81 = 9. √2 on the page is about 1.41421356. √0 = 0.
- √
- The root mark in this calculator. √81 = 9. √0.25 = 0.5. √0 = 0. A negative number does not run.
- √2
- The irrational example on the page, about 1.41421356. Not a whole number, unlike √81 = 9.
Examples
Example 2
- Number: 2
≈ 1.41421356
√2 is not a whole number - it is irrational.
Example 3
- Number: 0.25
0.5
0.5² = 0.25 - the root of a quarter is a half.
Example 4
- Number: 0
0
√0 = 0.
Example 5
- Number: 144
12
What is √144? 12, because 12 × 12 = 144.
Example 6
- Number: 256
16
What is √256? 16, because 16 × 16 = 256.
Example 7
- Number: 100
10
What is √100? 10, because 10 × 10 = 100.
Example 8
- Number: 0.01
0.1
What is √0.01? 0.1, because 0.1 × 0.1 = 0.01.
Related calculators
Frequently asked questions
What is √81?
9, because 9 × 9 = 81. That is a perfect square, so the result is an exact integer.
What is √2?
About 1.41421356. √2 is not an integer; it is irrational.
Is √0 = 0?
Yes. Zero times zero is zero, so a typed 0 runs and returns 0.
Why does √(−9) fail?
In the reals a negative has no square root. This calculator stays with the reals.
What are √16, √100, and √49?
4, 10, and 7. Those are perfect squares, so the results are whole numbers.
Does 6.25 give 2.5?
Yes. 2.5 × 2.5 = 6.25. A comma and a period both parse.
How is this different from the 1/2 power?
Same arithmetic. Here one Number field and the root at once. Power wants a base and an exponent.
Where is √(9+16) = 5?
On the Pythagorean theorem or on vector length (3, 4). Here you type one x.
What is √5?
About 2.23606798. Like √2, it is irrational, so the calculator keeps extra digits.
Can the result be negative?
No. The calculator uses the non-negative root. −9 also squares to 81, but here you keep 9.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.