Root Calculator
Calculate square roots, cube roots, or any other root of a number with ease. Simplify complex calculations and solve mathematical problems effortlessly using our versatile root calculator.
Square Root Calculator
Simplify square root calculations effortlessly. Get accurate results instantly for whole numbers, decimals, and negative numbers. Ideal for students, mathematicians, and professionals in various fields. Save time
Cube Root Calculator
Calculate the cube root of any number with our efficient Cube Root Calculator. Obtain precise results instantly, whether you're dealing with positive or negative numbers. Simply input the number and let the calculator do the rest. This tool is ideal for students, mathematicians, or anyone working with cube roots in various fields such as engineering, physics, or finance with the Cube Root Calculator.
General Root Calculator
Find the roots of any number with the General Root Calculator. Calculate square, cube, and higher roots effortlessly. Get accurate results instantly. Whether you need to find the square root, cube root, or any other root, this tool simplifies complex calculations with the General Root Calculator.
In mathematics, the general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:
n√a = b
bn = a
Estimating a Root
Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Calculating square roots and nth roots is fairly intensive. It requires estimation and trial and error. There exist more precise and efficient ways to calculate square roots, but below is a method that does not require a significant understanding of more complicated math concepts. To calculate √a:
- Estimate a number b
- Divide a by b. If the number c returned is precise to the desired decimal place, stop.
- Average b and c and use the result as a new guess
- Repeat step two
| EX: | Find √27 to 3 decimal places |
|
Guess: 5.125 27 ÷ 5.125 = 5.268 (5.125 + 5.268)/2 = 5.197 27 ÷ 5.197 = 5.195 (5.195 + 5.197)/2 = 5.196 27 ÷ 5.196 = 5.196 |
Estimating an nth Root
Calculating nth roots can be done using a similar method, with modifications to deal with n. While computing square roots entirely by hand is tedious. Estimating higher nth roots, even if using a calculator for intermediary steps, is significantly more tedious. For those with an understanding of series, refer here for a more mathematical algorithm for calculating nth roots. For a simpler, but less efficient method, continue to the following steps and example. To calculate n√a:
- Estimate a number b
- Divide a by bn-1. If the number c returned is precise to the desired decimal place, stop.
- Average: [b × (n-1) + c] / n
- Repeat step two
| EX: | Find 8√15 to 3 decimal places |
|
Guess: 1.432 15 ÷ 1.4327 = 1.405 (1.432 × 7 + 1.405)/8 = 1.388 15 ÷ 1.3887 = 1.403 (1.403 × 7 + 1.388)/8 = 1.402 |
It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.
Square roots table
| x | √x |
|---|---|
| 0 | 0 |
| 0.25 | 0.5 |
| 0.5 | 0.70710678 |
| 1 | 1 |
| 2 | 1.14121356 |
| 3 | 1.73205081 |
| 4 | 2 |
| 5 | 2.23606798 |
| 6 | 2.44948974 |
| 7 | 2.64575131 |
| 8 | 2.82842712 |
| 9 | 3 |
Root Calculator Example
| Number | Square Root | Cube Root | Fourth Root |
|---|---|---|---|
| 16 | 4 | 2 | 2 |
| 81 | 9 | 4.3267 | 3.0001 |
| 9 | 3 | 2.08 | 1.7321 |
| 25 | 5 | 2.92 | 2.2361 |
With the Root Calculator, you can find the square root, cube root, or fourth root of any number accurately and easily.
