Square Root of 41.8 = 6.4653

Square Root Calculator

Here is the answer to questions like: Square Root of 41.8 = 6.4653 (Step-by-Step Solution) or what is the square root of 41.8?

Use the square root calculator below to find the square root of any imaginary or real number. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method.

Step-by-Step: Babylonian Method

The Babylonian Method (also known as Hero's Method) is an iterative algorithm for computing square roots:

x_n+1 = (x_n + a/x_n) / 2

For a = 41.8, starting from x₀ = 20.9:

After 5 iterations: √41.8 ≈ 6.4653  (rounded to 4 decimal places).

The interactive calculator below uses a stricter convergence tolerance — see the full step-by-step output that appears once the page loads.

The Babylonian Method (Interactive)

See below how to calculate the square root of 41.8 step-by-step using the Babylonian Method (also known as Hero's Method).

Formula

The square root of a non-negative number a is the value x such that:

x² = a  ⇔  √a = x  (for x ≥ 0)

Every positive number has two square roots: a positive one (the principal root returned by this calculator) and a negative one. For example, √25 = 5 and also -5, since (-5)² = 25.

The square root of a negative number is not a real number — it is an imaginary number written as i√|a|.

What is a square root?

A square root of a number 'a' is a number x such that x² = a — a number whose square is a. For example, 6 is the square root of 36 because 6² = 6 · 6 = 36; and -6 is also a square root of 36 because (-6)² = (-6) · (-6) = 36.

Nearby Square Roots

Square Root Table 1-100

Square roots from 1 to 100 rounded to the nearest thousandth.

References

• [1] Babylonian method (Wikipedia)
• [2] Manually calculate the square root of a number with Javascript

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