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How to Make A 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 find square roots using calculators and manual methods, including step-by-step instructions and practical examples.

How to Calculate Square Roots

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. Calculating square roots can be done using calculators or manual methods.

Square Root Formula

For a positive real number a, the square root is written as √a. Mathematically, it satisfies the equation:

√a × √a = a

Key Properties of Square Roots

  • The square root of a negative number is not a real number (it's an imaginary number).
  • The square root of zero is zero.
  • The square root of a perfect square is an integer.
  • Square roots of non-square numbers are irrational.

Calculator Methods

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

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 (often labeled √ or √x).
  4. Press the equals (=) button to display the result.

Example: To find √25 on a scientific calculator:

  1. Enter 25
  2. Press √
  3. Press =
  4. Result: 5

Using a Graphing Calculator

Graphing calculators often have more advanced features, including the ability to calculate square roots of variables:

  1. Enter the expression, such as √(x² + 4x + 4).
  2. Use the solve function to find specific values.

Manual Calculation Methods

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

Prime Factorization Method

This method works well for perfect squares:

  1. Factor the number into its prime factors.
  2. Group the prime factors into pairs.
  3. Multiply one factor from each pair to get the square root.

Example: Find √36

  1. Prime factors of 36: 2 × 2 × 3 × 3
  2. Grouped pairs: (2 × 2) and (3 × 3)
  3. Square root: 2 × 3 = 6

Long Division Method

This method can find square roots of non-perfect squares:

  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 quotient and find a digit to append that makes the new number divisible by the new divisor.
  5. Repeat until desired precision is achieved.

Common Errors

Avoid these mistakes when calculating square roots:

  • Confusing square roots with squares: √9 = 3, not 9² = 81.
  • Forgetting to include the ± sign for negative numbers under the radical.
  • Using the wrong button on your calculator (e.g., pressing × instead of √).
  • Rounding too early in manual calculations.

Frequently Asked Questions

What is the difference between a square and a square root?

A square of a number is that number multiplied by itself (e.g., 5² = 25). A square root is a number that, when multiplied by itself, gives the original number (e.g., √25 = 5).

Can I find the square root of a negative number?

No, in real numbers, the square root of a negative number is not defined. However, in complex numbers, it's represented using the imaginary unit i (e.g., √-1 = i).

How do I calculate the square root of a fraction?

To find √(a/b), you can calculate it as √a / √b. For example, √(1/4) = √1 / √4 = 1/2.

What is the square root of zero?

The square root of zero is zero, since 0 × 0 = 0.

How do I calculate the square root of a decimal?

Use your calculator's decimal input or the long division method. For example, √2.25 = 1.5.