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Square Root Calculator Key

Reviewed by Calculator Editorial Team

The square root calculator key is a fundamental mathematical operation that finds the number which, when multiplied by itself, gives the original number. This guide explains how to use the square root key on your calculator, provides the mathematical formula, and includes practical examples.

How to use the square root key

Most scientific calculators have a dedicated square root key, typically labeled with a radical symbol (√) or "sqrt". Here's how to use it:

  1. Enter the number you want to find the square root of.
  2. Press the square root key (√).
  3. The calculator will display the square root of your number.

For example, to find the square root of 25:

  1. Press the "2" key, then the "5" key.
  2. Press the √ key.
  3. The calculator will display "5" as the result.

Note: If you enter a negative number, most calculators will display an error message. This is because the square root of a negative number is not a real number (it's an imaginary number).

Square root formula

The square root of a number x is a number y such that y² = x. Mathematically, this is represented as:

√x = y

where y² = x

For example, the square root of 16 is 4 because 4 × 4 = 16.

Square roots can be calculated using the following formula:

√x = x^(1/2)

This formula shows that the square root is equivalent to raising the number to the power of 1/2.

Worked examples

Example 1: Finding the square root of 36

To find the square root of 36:

  1. Enter 36 on your calculator.
  2. Press the √ key.
  3. The calculator will display "6" as the result.

Verification: 6 × 6 = 36, so the square root of 36 is indeed 6.

Example 2: Finding the square root of 0.25

To find the square root of 0.25:

  1. Enter 0.25 on your calculator.
  2. Press the √ key.
  3. The calculator will display "0.5" as the result.

Verification: 0.5 × 0.5 = 0.25, so the square root of 0.25 is indeed 0.5.

Example 3: Finding the square root of 100

To find the square root of 100:

  1. Enter 100 on your calculator.
  2. Press the √ key.
  3. The calculator will display "10" as the result.

Verification: 10 × 10 = 100, so the square root of 100 is indeed 10.

Frequently asked questions

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 the negative number. For example, the square root of -4 is 2i.

How do I calculate the square root of a fraction?

To calculate the square root of a fraction, take the square root of the numerator and the denominator separately. For example, √(1/4) = √1 / √4 = 1/2.

What is the difference between square root and square?

The square of a number is the result of multiplying the number by itself (x² = x × x). The square root is the inverse operation - finding a number that, when multiplied by itself, gives the original number (√x = y where y² = x).