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How To.find Square Root Witbkut Calculator

Reviewed by Calculator Editorial Team

Finding the square root of a number is a fundamental mathematical operation with applications in geometry, algebra, and many other fields. This guide explains how to accurately calculate square roots using a calculator, including step-by-step instructions, formulas, and practical examples.

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are represented with the radical symbol √.

Square roots can be either positive or negative, but by convention, the principal (or positive) square root is used unless specified otherwise. For example, √25 = 5, not ±5.

Square roots of non-perfect squares (numbers that aren't squares of integers) are irrational numbers, meaning they cannot be expressed as simple fractions and have non-repeating, non-terminating decimal expansions.

How to Use a Calculator for Square Roots

Most scientific and graphing calculators have a dedicated square root function. Here's how to use it:

  1. Turn on your calculator and clear any previous calculations.
  2. Enter the number you want to find the square root of.
  3. Press the square root button (often labeled √ or √x).
  4. Press the equals (=) button to display the result.

For example, to find √25:

  1. Enter 25 on your calculator.
  2. Press the √ button.
  3. Press = to see the result: 5.

If your calculator doesn't have a dedicated square root button, you can use the exponent function (often labeled y^x or ^) and enter 0.5 as the exponent. For example, to find √25, enter 25^(0.5).

Square Root Formula

The square root of a number x can be calculated using the following formula:

√x = x^(1/2)

Where:

  • √x is the square root of x
  • x is the number you want to find the square root of

Worked Examples

Example 1: Perfect Square

Find √36.

  1. Enter 36 on your calculator.
  2. Press the √ button.
  3. Press = to see the result: 6.

Verification: 6 × 6 = 36, so √36 = 6.

Example 2: Non-Perfect Square

Find √2.

  1. Enter 2 on your calculator.
  2. Press the √ button.
  3. Press = to see the result: 1.414213562...

Verification: 1.414213562 × 1.414213562 ≈ 2.

Example 3: Using Exponent Function

Find √16 using the exponent function.

  1. Enter 16 on your calculator.
  2. Press the exponent button (y^x or ^).
  3. Enter 0.5.
  4. Press = to see the result: 4.

Verification: 4 × 4 = 16, so √16 = 4.

Frequently Asked Questions

What is the difference between a square and a square root?
The square of a number is the result of multiplying the number by itself (e.g., 5² = 25). The square root of a number is a value that, when multiplied by itself, gives the original number (e.g., √25 = 5).
Can I find the square root of a negative number?
In real numbers, the square root of a negative number is not defined. However, in complex numbers, negative numbers have square roots that involve the imaginary unit i (e.g., √-1 = i).
What is the square root of zero?
The square root of zero is zero, because 0 × 0 = 0.
How do I find the square root of a fraction?
To find the square root of a fraction, find the square root of the numerator and the denominator separately. For example, √(1/4) = √1/√4 = 1/2.
What is the difference between √x and x^(1/2)?dt>
√x and x^(1/2) are mathematically equivalent expressions. Both represent the square root of x. The choice between them depends on the notation preferred by the calculator or the context of the problem.