Square Root Calculator
√
Calculate square roots, nth roots, simplify radicals, check perfect squares, and more. A complete toolkit for all your radical and root calculations.
| n | n² | √n² |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 2 |
| 3 | 9 | 3 |
| 4 | 16 | 4 |
| 5 | 25 | 5 |
| 6 | 36 | 6 |
| 7 | 49 | 7 |
| 8 | 64 | 8 |
| 9 | 81 | 9 |
| 10 | 100 | 10 |
| n | n² | √n² |
|---|---|---|
| 11 | 121 | 11 |
| 12 | 144 | 12 |
| 13 | 169 | 13 |
| 14 | 196 | 14 |
| 15 | 225 | 15 |
| 16 | 256 | 16 |
| 17 | 289 | 17 |
| 18 | 324 | 18 |
| 19 | 361 | 19 |
| 20 | 400 | 20 |
| n | n² | √n² |
|---|---|---|
| 21 | 441 | 21 |
| 22 | 484 | 22 |
| 23 | 529 | 23 |
| 24 | 576 | 24 |
| 25 | 625 | 25 |
| 30 | 900 | 30 |
| 40 | 1600 | 40 |
| 50 | 2500 | 50 |
| 100 | 10000 | 100 |
| 1000 | 1000000 | 1000 |
The square root of a is b if b squared equals a.
The root of a product equals the product of roots.
The root of a quotient equals the quotient of roots.
The square root of a squared is the absolute value.
Square root can be written as a fractional exponent.
Any root can be expressed as a fractional power.
Find the largest perfect square that divides into your number.
Separate the perfect square from the other factor.
Take the square root of the perfect square factor.
Express in simplified radical form: coefficient × √remaining
Find the hypotenuse: a² + b² = c²
Find the side of a square given its area
Distance between two points
Statistical measure of spread
Calculate TV/monitor diagonal size
RMS voltage calculations
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots: one positive (principal) and one negative.
Not in the real number system. The square root of a negative number involves imaginary numbers. For example, √(-1) = i (the imaginary unit). √(-9) = 3i.
A perfect square is an integer that is the square of another integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. Their square roots are whole numbers.
Factor the number inside the radical, find perfect square factors, take their root outside the radical. For example, √48 = √(16×3) = 4√3.
√ (square root) asks "what number squared equals this?" while ³√ (cube root) asks "what number cubed equals this?" √8 ≈ 2.83, but ³√8 = 2 (because 2³ = 8).
No, √2 is irrational. It cannot be expressed as a simple fraction and its decimal expansion never ends or repeats. √2 ≈ 1.41421356... This was proven by ancient Greek mathematicians.