How to Put Square Root of 3 in Calculator

Calculating the square root of 3 (√3) is a common mathematical operation with applications in geometry, trigonometry, and engineering. This guide explains how to input and calculate √3 using different methods, including standard calculators and manual techniques.

How to Calculate Square Root of 3

The square root of a number is a value that, when multiplied by itself, gives the original number. For 3, the square root is approximately 1.73205080757.

Formula

√3 = x, where x × x = 3

There are several ways to calculate √3:

Using a scientific calculator
Using a programming language (like Python or JavaScript)
Using the long division method manually

Using a Calculator

Most scientific calculators have a square root function that can compute √3 directly. Here's how to do it:

Step-by-Step Instructions

Turn on your calculator and clear any previous calculations.
Enter the number 3.
Press the square root (√) button.
The calculator will display the result: approximately 1.73205080757.

Tip

If your calculator doesn't have a dedicated √ button, you can use the exponent function (yˣ) by entering 3 and then 0.5 (since √3 = 3^(1/2)).

For example, on a calculator with an exponent function:

Enter 3.
Press the exponent (yˣ) button.
Enter 0.5.
Press the equals (=) button to get the result.

Manual Calculation

If you don't have a calculator, you can estimate √3 using the long division method or approximation techniques.

Long Division Method

The long division method involves a series of steps to find the square root:

Group the digits of 3 in pairs from right to left: 03.
Find the largest number whose square is less than or equal to 3. This is 1 (since 1 × 1 = 1).
Subtract 1 from 3 to get 2.
Bring down the next pair of zeros (00), making it 200.
Double the current result (1 × 2 = 2) and find a digit to place after the decimal point. We look for a digit d such that (20 + d) × d ≤ 200.
Testing d = 7: (20 + 7) × 7 = 27 × 7 = 189 ≤ 200.
Subtract 189 from 200 to get 11.
Bring down the next pair of zeros (00), making it 1100.
Double the current result (17 × 2 = 34) and find a digit to place next. We look for a digit d such that (340 + d) × d ≤ 1100.
Testing d = 3: (340 + 3) × 3 = 343 × 3 = 1029 ≤ 1100.
Subtract 1029 from 1100 to get 71.
This process continues, yielding more decimal places.

The manual calculation gives √3 ≈ 1.73205080757, which matches the calculator result.

Note

Manual calculation is time-consuming and prone to error. For most practical purposes, using a calculator is recommended.

Common Uses of √3

The square root of 3 appears in various mathematical and real-world applications:

Geometry: In equilateral triangles, the ratio of the height to the side length is √3/2.
Trigonometry: The tangent of 60 degrees (π/3 radians) is √3.
Engineering: Used in calculations involving 30-60-90 triangles and other geometric problems.
Physics: Appears in wave functions and other mathematical models.

Understanding how to calculate √3 is essential for solving problems in these fields.

FAQ

How do I calculate √3 on a basic calculator?: Most basic calculators don't have a √ button. You can use the exponent function by entering 3, then 0.5, and pressing equals.
Is √3 a rational or irrational number?: √3 is an irrational number because it cannot be expressed as a simple fraction and its decimal representation is non-terminating and non-repeating.
What is the exact value of √3?: The exact value of √3 is √3, which is approximately 1.73205080757.
Where is √3 used in real life?: √3 is used in geometry (equilateral triangles), trigonometry (tangent of 60°), and engineering calculations involving 30-60-90 triangles.
Can I calculate √3 without a calculator?: Yes, you can use the long division method or approximation techniques, but it's time-consuming and less precise than using a calculator.