Square Root Chart Calculator

The square root of a number is a value that, when multiplied by itself, gives the original number. This calculator helps you find square roots and visualize them with an interactive chart.

What is Square Root?

The square root of a number x is a number y such that y² = x. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are used in many mathematical applications, including geometry, algebra, and calculus.

Square roots can be positive or negative, but the principal (or positive) square root is typically used in most calculations. For example, the square roots of 9 are 3 and -3, but we usually consider √9 = 3.

How to Calculate Square Root

There are several methods to calculate square roots:

Prime Factorization Method: Break down the number into its prime factors, then pair the factors and take one from each pair.
Long Division Method: A more complex method involving repeated division and estimation.
Using a Calculator: The quickest method for most practical purposes.

Our calculator uses JavaScript's built-in Math.sqrt() function for accurate and efficient calculations.

Square Root Formula

The square root of a number x can be represented as:

√x = y

Where y × y = x

For example, √16 = 4 because 4 × 4 = 16.

Square Root Chart

The chart below shows the relationship between numbers and their square roots. You can use the calculator to generate points on this chart.

The chart displays the square root function y = √x for x ≥ 0. The curve shows how square roots grow at a decreasing rate as x increases.

Square Root Examples

Here are some examples of square roots:

√4 = 2 (since 2 × 2 = 4)
√9 = 3 (since 3 × 3 = 9)
√16 = 4 (since 4 × 4 = 16)
√25 = 5 (since 5 × 5 = 25)
√36 = 6 (since 6 × 6 = 36)

Try these examples in our calculator to see how they work.

Square Root FAQ

What is the square root of 0?: The square root of 0 is 0 because 0 × 0 = 0.
What is the square root of 1?: The square root of 1 is 1 because 1 × 1 = 1.
What is the square root of a negative number?: The square root of a negative number is not a real number. It's an imaginary number, represented as i√x where x is positive.
How do I calculate the square root of a fraction?: To find the square root of a fraction a/b, take the square root of the numerator and the denominator separately: √(a/b) = √a / √b.
What is the difference between square root and square?: The square of a number is that number multiplied by itself (x² = x × x). The square root is the inverse operation that finds a number which, when multiplied by itself, gives the original number.