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How to Put in Square Root on Calculator

Reviewed by Calculator Editorial Team

Calculating square roots is a fundamental math operation with applications in geometry, algebra, and many scientific fields. This guide explains how to properly input and interpret square roots on different types of calculators, including scientific, graphing, and smartphone calculators.

How to Calculate Square Roots

Square roots are the inverse operation of squaring a number. The square root of a number x is a value that, when multiplied by itself, gives x. Mathematically, this is represented as √x.

Square Root Formula

For a positive real number x, the square root is defined as:

√x = y where y × y = x

For example, √9 = 3 because 3 × 3 = 9.

Basic Steps for Calculator Input

  1. Turn on your calculator and clear any previous calculations.
  2. Enter the number you want to find the square root of.
  3. Locate the square root function button (often labeled with √ or a radical symbol).
  4. Press the square root button to calculate the result.
  5. Review the result and verify it makes sense in your context.

Important Notes

  • Most calculators will show both positive and negative roots when solving equations.
  • Square roots of negative numbers are not real numbers but complex numbers.
  • Always check your calculator's mode (degrees vs radians) if you're working with trigonometric functions.

Different Calculator Methods

Calculators vary in how they handle square root calculations. Here are the most common methods:

Scientific Calculator Method

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

Graphing Calculator Method

  1. Enter the equation in the form of y = √(x)
  2. Use the graphing function to visualize the square root function
  3. For specific values, use the table function to evaluate at particular x-values

Smartphone Calculator Method

  1. Open your calculator app
  2. Enter the number you want to find the square root of
  3. Tap the square root button (√)
  4. View the result

Example Calculation

Find √16 using a scientific calculator:

  1. Press the √ button
  2. Enter 16
  3. Press =
  4. Result: 4

Common Mistakes to Avoid

When working with square roots, these common errors can lead to incorrect results:

Mistake 1: Forgetting to Press the Square Root Button

Many users simply enter the number and press equals without using the √ function, resulting in the original number rather than its square root.

Mistake 2: Incorrect Order of Operations

When combining square roots with other operations, remember that square roots have higher precedence than multiplication and addition.

Mistake 3: Negative Number Input

Attempting to find the square root of a negative number on a basic calculator will result in an error. Use a scientific calculator for complex numbers.

Pro Tip

Always double-check your input and verify the result by squaring it to ensure you've calculated the correct square root.

Real-World Examples

Square roots have practical applications in various fields:

Geometry Example

If you have a square with an area of 25 square units, the length of each side is √25 = 5 units.

Algebra Example

Solving x² = 16 gives x = ±√16 = ±4.

Physics Example

When calculating the velocity of an object, square roots are used in kinematic equations like v = √(2gh).

Square Root Applications
Field Application Example
Geometry Finding side lengths √(area) = side length
Algebra Solving quadratic equations x = ±√(b² - 4ac)
Physics Kinematic calculations v = √(2gh)

Frequently Asked Questions

What is the difference between √ and √²?

√ represents the square root function, while √² means the square of the square root. For example, √9 = 3 and √²9 = (√9)² = 9.

Can I find the square root of a negative number?

On basic calculators, no. You need a scientific calculator that supports complex numbers to find the square root of negative numbers.

How do I calculate the square root of a fraction?

Enter the fraction, then press the square root button. For example, √(1/4) = 1/2.

What if my calculator shows an error for square roots?

Check that you've entered a valid number and pressed the square root button before equals. For negative numbers, ensure your calculator is in complex number mode.