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How to Work Out Square Root on A Calculator

Reviewed by Calculator Editorial Team

Calculating square roots is a fundamental mathematical operation with applications in geometry, algebra, and many scientific fields. This guide explains how to work out square roots using both calculator methods and manual techniques.

How to Calculate 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 25 is 5 because 5 × 5 = 25.

Square Root Formula:
√x = y where y × y = x

Square roots can be calculated using:

  • Scientific calculators
  • Graphing calculators
  • Programming calculators
  • Computer algebra systems
  • Manual calculation methods

Most modern calculators have a dedicated square root function, typically represented by the √ symbol. This guide focuses on using this function correctly.

Calculator Methods

Using a Scientific Calculator

  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.
  4. Press the = (equals) button to display the result.

Tip: Some calculators require you to press the √ button before entering the number. Check your calculator's manual if you're unsure.

Using a Graphing Calculator

Graphing calculators typically have a more advanced interface but follow similar steps:

  1. Enter the number in the input field.
  2. Select the square root function from the function menu.
  3. Execute the calculation.

Using a Computer Algebra System

For more complex calculations, you might use software like Mathematica or Maple:

  1. Open your CAS software.
  2. Type the command for square root (e.g., "sqrt(25)" in Mathematica).
  3. Run the command to get the result.

Manual Calculation Methods

While calculators are convenient, understanding manual methods can be helpful for verification or when a calculator isn't available.

Prime Factorization Method

  1. Factorize the number into its prime factors.
  2. Group the prime factors into pairs.
  3. Multiply the numbers in each pair.
  4. Multiply the results of the pairs to get the square root.

Example: Find √36

  1. 36 = 2 × 2 × 3 × 3
  2. Group into pairs: (2 × 2) and (3 × 3)
  3. Multiply pairs: 2 × 3 = 6
  4. Result: √36 = 6

Long Division Method

This method is more complex but works for any number:

  1. Group digits in pairs from the decimal point.
  2. Find the largest number whose square is less than or equal to the first group.
  3. Subtract and bring down the next pair.
  4. Double the current result and find a digit to append that makes the new number divisible by the doubled result.
  5. Repeat until desired precision is reached.

Note: Manual methods are time-consuming and prone to error. Calculators are generally more efficient for most practical purposes.

Common Mistakes

Avoid these common errors when calculating square roots:

  • Entering the number incorrectly
  • Pressing the wrong function key (e.g., using × instead of √)
  • Forgetting to press the equals button
  • Misinterpreting the result (e.g., confusing √4 with 4)
  • Using the wrong mode (e.g., degrees instead of radians)

Always double-check your input and verify the result by squaring it to ensure you get back to the original number.

FAQ

What is the square root symbol called?
The square root symbol is called a radical sign. It consists of a check mark with a horizontal line through the top, resembling a square root.
Can I calculate square roots of negative numbers?
In real numbers, the square root of a negative number is not defined. However, in complex numbers, negative numbers have square roots that involve imaginary numbers (i).
What is the difference between √ and ∛?
√ represents the square root (second root), while ∛ represents the cube root. The square root of a number is a value that, when multiplied by itself, gives the original number. The cube root is a value that, when multiplied by itself three times, gives the original number.
How do I calculate the square root of a fraction?
To find the square root of a fraction, take the square root of the numerator and the denominator separately. For example, √(a/b) = √a / √b.
What is the square root of zero?
The square root of zero is zero, because 0 × 0 = 0.