Square Root Formula Explained, With Examples
Every square root result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
√x is the number that multiplied by itself gives x.
What each input means
- Number: the value you enter in the calculator.
Example
For example, with these inputs:
- Number: 50
the calculator returns:
- √x: 7.0711
How the result changes
The table keeps the other inputs at their example values and changes number.
| Number | √x |
|---|---|
| 50 | 7.0711 |
| 25 | 5 |
| 37.5 | 6.1237 |
| 62.5 | 7.9057 |
| 75 | 8.6603 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
Related calculations
- Perimeter of an Ellipse Calculator: Calculates the perimeter of an ellipse from the measurements you enter.
- Arc Length Calculator: Calculates the arc length from the measurements you enter.
- Volume of a Cube Calculator: Calculates the volume of a cube from the measurements you enter.
- Volume of a Cuboid Calculator: Calculates the volume of a cuboid from the measurements you enter.
Use the Square Root Calculator to plug in your own numbers.
Run your own numbers: Square Root Calculator