The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 * 4 = 16. Mathematically, this is represented as:
If y = sqrt(x), then y * y = x.
This calculator focuses on the principal (non-negative) square root. The square root function is fundamental in various fields, including:
Mathematics: Solving quadratic equations, geometry (Pythagorean theorem), and calculus.
Physics: Calculating magnitudes of vectors, distances, and certain physical laws where quantities are squared.
Engineering: Signal processing, structural analysis, and electrical engineering calculations.
Statistics: Calculating standard deviations and other measures of dispersion.
How this Calculator Works
This calculator takes a single numerical input. It then uses JavaScript's built-in Math.sqrt() function to compute the principal square root of that number.
Input: A non-negative number.
Process:
The value entered into the "Enter Number" field is retrieved.
It's checked to ensure it's a valid, non-negative number.
The Math.sqrt() function is applied to the number.
Output: The calculated square root, displayed below. If the input is invalid (e.g., negative or not a number), an appropriate message is shown.
Example Calculation:
Let's say you input the number 25 into the "Enter Number" field.
Input Number: 25
Calculation: Math.sqrt(25)
Result: 5
Another example, inputting 2:
Input Number: 2
Calculation: Math.sqrt(2)
Result: Approximately 1.41421356237
Note that the square root of numbers that are not perfect squares will result in irrational numbers, which are displayed to a high degree of precision.
function calculateSquareRoot() {
var numberInput = document.getElementById("numberToCalculate");
var resultDiv = document.getElementById("result");
var numberValue = parseFloat(numberInput.value);
// Clear previous result/error message
resultDiv.textContent = "";
// Input validation
if (isNaN(numberValue)) {
resultDiv.textContent = "Error: Please enter a valid number.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
return;
}
if (numberValue < 0) {
resultDiv.textContent = "Error: Cannot calculate square root of a negative number.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
return;
}
// Perform calculation
var squareRoot = Math.sqrt(numberValue);
// Display result
resultDiv.textContent = "√" + numberValue + " = " + squareRoot.toFixed(10); // Display with precision
resultDiv.style.backgroundColor = getComputedStyle(document.documentElement).getPropertyValue('–success-green').trim(); // Reset to success green
}