Square Root of 6

Square Root of 6 is 2.449489742. The square root of a number is a value that, when multiplied by itself, results in the original number. This means if we multiply 2.449489742 by itself, the product will be approximately equal to 6.

In this article, we will learn what is square root of 6, how to find it using various methods, and some related facts.

Root 6 Value

What is Square Root of 6?

Square root of 6, denoted as √6, is an irrational number. The approximate numerical value of √6 is given below

√6 = 2.449489742…..

For practical purposes, it is often rounded to a few decimal places, such as 2.45.

Root 6 Value

Square root 6 is represented in various forms and the value of root 6 is,

Radical Form: √6 = 2.449489742…..

Exponential Form: (6)^1/2 = 2.449489742…..

How to Find Square Root of 6?

We can find square root of 6 using the following two methods:

• Root 6 Vlaue Long Division Method

• Root 6 Vlaue Prime Factorization Method

Square Root of 6 using Long Division Method

Follow the following mentioned steps to find the square root of 6 using the long division method

Step 1: Start with the number 6.000000 and start pairing its from right to left

Step 2: Choose a perfect square less than 6 as the initial dividend (e.g., 4). Hence divisor will be 2.

Step 3: Since, divisor is 2, quotient is 2 therefore dividend will be 4. Subtract 4 from 6 and add 2 in the divisor

Step 4: New divisor is 4, dividend is 2. Now put decimal after 2 in quotient and bring down two zeros. Therefore new dividend is 200

Step 5: Add a digit at left of 4 in divisor i.e. at unit place and also place the same digit in quotient such that the product is near to 200.

Step 6: Add 4 in divisor using step 5 hence, new dividend will be 44 × 4 = 176. Subtract 176 from 200

Step 7: Repeat the steps 4, 5 and 6 to find square root up to 3 or 4 decimal places as per requirement.

Learn, Square Root by Long Division

Square Root of 6 using Prime Factorization Method

Follow the steps mentioned below to find the square root of 6 using prime factorization method:

Steps 1: Break down 6 into its prime factors (2 × 3).

Steps 2: Use the prime factors to deduce the square root i.e. √6 = √(2 × 3) = √2 × √3

Steps 3: Multiply the value of square root of 2 and 3 to obtain square root of 6 which is given as 1.41421 × 1.7320 = 2.449

Learn, Prime Factorization Method

Is Square Root of 6 Rational or Irrational?

The square root of 6 is an irrational number. The square root of 6 is 2.44948974278… Since, this decimal expansion is a non terminating andThe decimal expansion of √6 goes on infinitely without repeating.

Square Root 6 Value Calculation – FAQs

What is Root 6 Value?

The square root of 6, denoted as √6, is approximately 2.45.

Why is Square Root of 6 an Irrational Number?

√6 is irrational because it cannot be expressed as a fraction of two integers.

Is the Number 6 a Perfect Square?

No, 6 is not a perfect square because it cannot be expressed as the square of an integer.

Does a Square Root Have Two Values?

Yes, a square root can have two values, one positive and one negative. For √, this means approximately ±2.45.