Value of Root 3

 

Understanding the value of root 3 is a basic concept in mathematics. This is especially true when working with irrational numbers, geometry, and trigonometry. The square root of 3, or √3, is common in mathematical problems, particularly those involving equilateral triangles, 30°-60°-90° triangles, and various engineering tasks.  

This topic explores the value of root 3 in-depth, providing explanations, methods to calculate it manually, and a clear breakdown using a square root table and the square root using long division method

 

Table of Contents

• Root 3 Value in Maths
• How to Find the Value of Root 3?
  • By Estimation
  • Square Root Using Long Division Method
• Value of Root 3 Explained
• Table of Square Root
• Practical Uses of √3 Value
• Conclusion
• FAQs On Value of Root 3

 

Root 3 Value in Maths  

In mathematics, the value of root 3 is the positive number that, when multiplied by itself, equals 3. Mathematically:  

√3 × √3 = 3  

The square root of 3 is an irrational number, which means it cannot be expressed as a simple fraction. Its decimal representation goes on infinitely without repeating. The approximate value of √3 is:  

√3 ≈ 1.7320508075  

This value is often used in trigonometry. For instance:  

• In a 30°-60°-90° triangle, the ratio of the sides includes the square root of 3.  

• The tangent of 60° equals the value of root 3.  

• The height of an equilateral triangle with side length ‘a’ is (√3/2) × a. 

 

How to Find the Value of Root 3?  

You might wonder how to find square root of 3 manually or without a calculator. There are several methods:  

1. By Estimation:  

Estimate between perfect squares:  

√1 = 1  

√4 = 2  

So, the square root of 3 lies between 1 and 2. Try estimating:  

1.7² = 2.89  

1.73² = 2.9929  

1.732² = 2.999824  

Thus, the value of √3 is approximately 1.732.  

 

2. Square Root Using Long Division Method:  

One reliable manual technique to find the value of root 3 is the long division method. Here are the steps:  

• Write 3 as 3.000000…  

• Group digits in pairs from the decimal point.  

• Find the largest number whose square is less than or equal to 3.  

• Use long division to expand digit by digit.  

Using this long division method, you can get the value of root 3 accurate to as many decimal places as needed.  

 

Value of Root 3  

Here are some key points about the value of root 3:  

• It is irrational.  

• Decimal approximation: √3 ≈ 1.732050807568877  

• √3 × √3 = 3  

• It is commonly used in geometry, trigonometry, and engineering.  

• By using the long division method, you can calculate the √3 value to more decimal places if needed.  

 

Table of Square Root  

The square root table below gives approximate values of common square roots. It is especially helpful for solving problems manually.  

As shown in the square root table, the value of root 3 falls between √2 and √4. This table offers a quick reference for commonly used √ values, with √3 value among the most frequently encountered.

 

Practical Uses of √3 Value  

The value of root 3 appears in many real-life applications:  

• Calculating heights and lengths in architecture  

• Electrical engineering (three-phase current systems)  

• Trigonometry (sine and tangent for 60°)  

• Physics (vector analysis) 

Knowing how to find the square root of 3 manually using estimation or the long division method is beneficial for both academic and practical problem-solving.  

 

Conclusion  

The value of root 3 is a key mathematical constant used in geometry, trigonometry, and many scientific fields. The square root of 3 is approximately 1.732 and is irrational, meaning it cannot be expressed exactly as a fraction. You can determine the value of √3 manually through estimation, the long division method, or by referring to a square root table.  

Understanding how to find square root of 3 will help you in solving a wide range of problems. Whether you're working in math, science, or engineering, the value of root 3 is an essential part of your toolkit.  

 

Related Links

Inverse Trigonometric Functions - Understand the concept of inverse trigonometric functions, their domains, ranges, and applications with solved examples.

Trigonometric Identities - Learn essential trigonometric identities, including reciprocal, Pythagorean, and co-function identities, with proofs and examples for better understanding.

Trigonometry - Explore the basics of trigonometry, including trigonometric ratios, applications, and problem-solving techniques with real-world context.

 

Frequently Asked Questions on Square Roots  

1. What is √3 of value?  

 Ans: The value of √3 (square root of 3) is approximately 1.732. It is an irrational number and cannot be expressed exactly as a simple fraction.  

 

2. What is √2 of value?

 Ans: The value of √2 (square root of 2) is approximately 1.414. Like √3, it is also an irrational number.  

 

3. How to solve √3? 

Ans: To solve or estimate √3 manually, you can use methods like long division, approximation, or a calculator. One way to estimate is by trying successive squares:  

   For example,  

   1.7² = 2.89  

   1.73² = 2.9929  

   1.732² ≈ 3.0001 → So √3 ≈ 1.732  

 

4. How to find √5 value? 

Ans: The value of √5 (square root of 5) is approximately 2.236. You can find it using a calculator or by using estimation methods similar to those used for √3.  

 

Learn how to calculate and apply the value of root 3 with step-by-step guidance from Orchids The International School!