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How to Get Square Root on Maths Calculator

Reviewed by Calculator Editorial Team

Calculating square roots is a fundamental math operation with applications in geometry, algebra, and many other fields. This guide explains how to find square roots using both calculators and manual methods, along with practical examples and troubleshooting tips.

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

For a positive real number x, the square root is denoted as √x and satisfies the equation:

√x × √x = x

Square roots can be calculated using:

  • Scientific calculators
  • Graphing calculators
  • Programming languages (Python, JavaScript, etc.)
  • Manual calculation methods

Using a Calculator

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

Step-by-Step Instructions

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

Tip

If your calculator doesn't have a dedicated square root button, you can calculate it using the exponent function (x1/2).

Example Calculation

Let's find the square root of 144:

  1. Enter 144 on your calculator.
  2. Press the √ button.
  3. The result will be 12, since 12 × 12 = 144.

Manual Calculation Methods

If you don't have a calculator, you can estimate square roots using these methods:

Prime Factorization Method

  1. Factorize 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: Square Root of 72

  1. Factorize 72: 2 × 2 × 2 × 3 × 3
  2. Group into pairs: (2 × 2) × (2 × 3) × 3
  3. Multiply one from each pair: 2 × 3 = 6
  4. So, √72 ≈ 6√2 ≈ 8.485

Long Division Method

This method is more precise but requires more steps:

  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 achieved.

Common Mistakes

Avoid these errors when calculating square roots:

  • Forgetting to pair digits properly in long division
  • Miscounting prime factors in factorization
  • Using the wrong exponent (e.g., x2 instead of x1/2)
  • Assuming all numbers have perfect square roots

Important Note

Square roots of negative numbers are not real numbers. For example, √-1 is an imaginary number (i).

Practical Examples

Square roots have many real-world applications:

Geometry

Finding the side length of a square when you know the area.

Algebra

Solving quadratic equations and simplifying expressions.

Physics

Calculating distances and velocities in motion problems.

Finance

Determining standard deviations in statistical analysis.

FAQ

What is the square root of zero?
The square root of zero is zero, since 0 × 0 = 0.
Can I calculate square roots of negative numbers?
In real numbers, no. Square roots of negative numbers are imaginary numbers (e.g., √-1 = i).
How do I calculate the square root of a fraction?
Take the square root of the numerator and denominator separately: √(a/b) = √a / √b.
What's the difference between √ and √√?
√ is the principal (non-negative) square root. √√ is the fourth root (√√x = x^(1/4)).
How accurate are calculator square roots?
Most scientific calculators provide 10-12 decimal places of accuracy for square roots.