Square Root Calculator

Square Root

Square root of x:

square root = √x

Cube root

The cube root of x is given by the formula:

cube root = 3x

3

n'th root

The nth root of x is given by the formula:

nth root = nx

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 significant understanding of more complicated math concepts. To calculate √a:

1. Estimate a number b
2. Divide a by b. If the number c returned is precise to the desired decimal place, stop.
3. Average b and c and use the result as a new guess
4. Repeat step two
 EX: Find √27 to 3 decimal places Guess: 5.12527 ÷ 5.125 = 5.268(5.125 + 5.268)/2 = 5.19727 ÷ 5.197 = 5.195(5.195 + 5.197)/2 = 5.19627 ÷ 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:

1. Estimate a number b
2. Divide a by bn-1. If the number c returned is precise to the desired decimal place, stop.
3. Average: [b × (n-1) + c] / n
4. Repeat step two
 EX: Find 8√15 to 3 decimal places Guess: 1.43215 ÷ 1.4327 = 1.405(1.432 × 7 + 1.405)/8 = 1.38815 ÷ 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.

Policy for Use of Square Root Calculator

1. All the data is safe and secure
2. Ovdss is never responsible to any unwanted activity make by user.
3. Adhere to all local, state, and federal laws while using the tool.
4. Engage respectfully with other users; no harassment, bullying, or hate speech.
5. Respect copyright and intellectual property rights; do not share unauthorized content.
6. Report any bugs, violations, or inappropriate behavior using the feedback option in this page.
7. Contributions (reviews, comments, etc.) should be honest and constructive.
8. Ensure your device meets this tool minimum requirements for optimal performance.
9. Respect and protect the privacy of other users; do not share personal information without consent.
10. Minors or people below 13 years old are not allowed to use this tool.
11. Restriction on using this tool in violation of applicable laws and regulations, or in any manner that may cause harm to any person, or any business entity.
These points help in creating a safe, respectful, and efficient environment for all users of the tool.

3.0(50)
Published Date: 09-06-2021
Updated Date: 20-07-2024
Developer: Ovdss Internal