Square Root Calculator
The square root of 144 is 12. This square root calculator finds the principal (positive) root of any non-negative number. Enter a value to see its square root, the matching negative root, and whether the number is a perfect square. Real square roots need a non-negative number, so the input cannot be less than zero.
Quick answer
The square root of a number is the value that, when multiplied by itself, gives that number.
What this tells you
- •The square root of a number is the value that, when multiplied by itself, gives that number.
- •Every positive number has two square roots, one positive and one negative, with the same size.
- •The principal square root is the non-negative one, so the square root of 144 is 12.
- •Results are rounded to 6 decimal places.
How to Use
- 1Enter the number you want the square root of in the Number field.
- 2Use a value of zero or greater, since negative numbers have no real square root.
- 3Click Calculate to see the square root, the negative root, and the perfect square check.
How It Works
Formula
sqrt(x) = y, where y * y = xThe square root of x is the number y that you multiply by itself to get back to x. For example, sqrt(144) = 12 because 12 * 12 = 144. The principal square root is the non-negative answer, and its opposite is the negative root.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Square root of 144
Find the value that multiplies by itself to give 144. Since 12 * 12 = 144, the square root of 144 is 12. The number is a perfect square because 12 is a whole number.
Square root of 2
There is no whole number that multiplies by itself to give 2, so the result is irrational. Rounded to 6 decimal places, the square root of 2 is about 1.414214, which means 2 is not a perfect square.
Perfect Squares and Their Roots
Common perfect squares and the whole number square root of each.
| Number | Square Root |
|---|---|
| 4 | 2 |
| 9 | 3 |
| 16 | 4 |
| 25 | 5 |
| 36 | 6 |
| 64 | 8 |
| 100 | 10 |
| 144 | 12 |
Common mistakes
- Trying to take the square root of a negative number. Negative numbers have no real square root, so this calculator returns no result for values below zero.
- Confusing squaring with square rooting. Squaring multiplies a number by itself, while finding a square root reverses that step, so the two operations are not the same.
- Ignoring that every positive number has two roots. Both a positive and a negative value square to the same number, so 25 has the roots 5 and -5.