Square Root of 4489 = 67

Square Root Calculator

Here is the answer to questions like: Square Root of 4489 = 67 (Step-by-Step Solution) or what is the square root of 4489?

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.

4489 Is a Perfect Square

√4489 = 67  because  67² = 67 × 67 = 4489

The Babylonian Method (Interactive)

See below how to calculate the square root of 4489 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, 67 is the square root of 4489 because 67² = 67 · 67 = 4489; and -67 is also a square root of 4489 because (-67)² = (-67) · (-67) = 4489.

Nearby Square Roots

Square Root Table 1-100

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

Related Operations

Simplified radical form: Try our Simplify Square Root Calculator to see √4489 in simplest form (e.g. 5√2 instead of 7.0711…).

Inverse operation: Since √4489 = 67, the inverse is squaring: 67² = 4489. See our Squared Calculator.

References

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

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