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Symbol for Square Root on A Calculator

Reviewed by Calculator Editorial Team

The square root symbol is a fundamental mathematical notation used in calculators and mathematical expressions. This guide explains what the symbol represents, how to use it, its historical development, and common misconceptions about square roots.

What is the Square Root Symbol?

The square root symbol, represented as √, is a mathematical operator that indicates the principal (non-negative) square root of a number. For example, √9 = 3 because 3 × 3 = 9.

In calculators, the square root symbol is typically found on the scientific or advanced function keys. It's used to find the square root of any positive real number.

Square Root Formula

For a non-negative real number a, the square root is defined as:

√a = b where b × b = a and b ≥ 0

How to Use the Square Root Symbol

Using the square root symbol on a calculator is straightforward:

  1. Enter the number you want to find the square root of.
  2. Press the square root button (√).
  3. Press the equals (=) button to get the result.

For example, to find √16:

  1. Enter "16".
  2. Press √.
  3. Press = to get "4".

Note

Most calculators will display an error if you try to find the square root of a negative number, as square roots of negative numbers are not real numbers (they are complex numbers).

History of the Square Root Symbol

The square root symbol has evolved over time. The modern radical symbol (√) was first used by Christian Rudolff in his 1525 book "Coss".

Before this, mathematicians used various notations, including a small letter "r" (for radix) placed before the number, or a horizontal line over the number.

In the 17th century, René Descartes popularized the use of the radical symbol, which became widely adopted in the 18th century.

Common Misconceptions

There are several common misunderstandings about square roots:

  • Square root of a negative number: While the square root of a negative number isn't a real number, it does have a complex number solution.
  • Multiple square roots: Every positive number has two square roots: one positive and one negative. For example, both 3 and -3 are square roots of 9.
  • Square root vs. square: The square root of a number is not the same as squaring a number. The square root of 4 is 2, while 4 squared is 16.

FAQ

What does the √ symbol mean?

The √ symbol represents the square root function, which finds the number that, when multiplied by itself, gives the original number.

Can I find the square root of a negative number?

On most calculators, you'll get an error when trying to find the square root of a negative number. However, in advanced mathematics, negative numbers have complex square roots.

What's the difference between √ and ²?

√ is the square root symbol, while ² is the exponent for squaring a number. For example, 3² = 9, while √9 = 3.