Square Root Calculator
By Santaji GadepatilinUpdated October 27, 2026
A square root is the number that, multiplied by itself, gives the original number. Square roots appear in geometry, statistics and physics.
How to use the square root calculator
Enter any non-negative number to see its square root, cube root and square. It works backwards too: type a value in Square root and the original number is calculated.
Perfect squares and cubes
| n | n² | n³ | n | n² | n³ |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 11 | 121 | 1,331 |
| 2 | 4 | 8 | 12 | 144 | 1,728 |
| 3 | 9 | 27 | 13 | 169 | 2,197 |
| 4 | 16 | 64 | 14 | 196 | 2,744 |
| 5 | 25 | 125 | 15 | 225 | 3,375 |
| 6 | 36 | 216 | 16 | 256 | 4,096 |
| 7 | 49 | 343 | 17 | 289 | 4,913 |
| 8 | 64 | 512 | 18 | 324 | 5,832 |
| 9 | 81 | 729 | 19 | 361 | 6,859 |
| 10 | 100 | 1000 | 20 | 400 | 8,000 |
Square roots of 1 to 20
| x | √x | x | √x |
|---|---|---|---|
| 1 | 1.0000 | 11 | 3.3166 |
| 2 | 1.4142 | 12 | 3.4641 |
| 3 | 1.7321 | 13 | 3.6056 |
| 4 | 2.0000 | 14 | 3.7417 |
| 5 | 2.2361 | 15 | 3.8730 |
| 6 | 2.4495 | 16 | 4.0000 |
| 7 | 2.6458 | 17 | 4.1231 |
| 8 | 2.8284 | 18 | 4.2426 |
| 9 | 3.0000 | 19 | 4.3589 |
| 10 | 3.1623 | 20 | 4.4721 |
Simplifying square roots
Look for the largest perfect-square factor:
- √50 = √(25 × 2) = 5√2
- √72 = √(36 × 2) = 6√2
- √48 = √(16 × 3) = 4√3
Estimating by hand
Find the two perfect squares around the number. √50 lies between √49 = 7 and √64 = 8, much closer to 7. A first estimate of 7.07 is accurate to two decimals.
Newton’s method refines any guess g: new g = (g + x ÷ g) ÷ 2. Starting from 7 for √50: (7 + 50/7) ÷ 2 = 7.0714 — already correct to four decimal places.
Rules for roots
- √(a × b) = √a × √b
- √(a ÷ b) = √a ÷ √b
- √a + √b is not √(a + b)
- x1/2 = √x and x1/3 = ∛x
Where square roots appear
The Pythagorean theorem, standard deviation, the quadratic formula, circle radius from area and RMS voltage all use square roots.
Frequently asked questions
What is the square root of 50?
About 7.0711. In simplest radical form, √50 = 5√2.
Can I find the number from its square root?
Yes. Press × on Number and type the square root — the calculator squares it.
What is the square root of a negative number?
It is not a real number. √−1 is the imaginary unit i, so √−9 = 3i.
What are perfect squares?
Whole numbers whose square roots are whole numbers, such as 1, 4, 9, 16, 25 and 36.