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Square Root of 6

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Last updated date: 17th Apr 2024
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Root 6 Value

The square root is a topic that many students find difficult to understand. However, once you understand the concept well, finding square roots will no longer be a challenge for you. So, in simple words square root, in mathematics, is a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.


The square root of a number a is the number b such that b² = a. The square root of any number is represented by the symbol and is also often known as radical. The number or expression given under the square root symbol is known as radicand. The square root is a commonly used function in Mathematics. It is widely used in subjects like Mathematics and Physics. Sometimes it is tedious to find the square root of a number, especially the numbers which are not the perfect square of the number. In this article, we will discuss the square root of 6, and how to calculate the root 6 value using the simplifying square root method.


What is the root 6 value?


The root 6 value is 2.449


Square Root of 6 Definition

The square root of a number 6 is a number y such that y² = 6. The square root of 6 in radical form is written as √6. The square root of 6 in radical form is expressed as√6


How to Calculate the Under Root 6 Value?

We can calculate the under root 6 value using different methods of square roots. These methods can be the long division methods, prime factorization method, or simplifying square root method. Let us discuss how to calculate the under root 6 value using the simplifying square root method.


To simplify a square root, make the number under the square root as small as possible while keeping it as a whole number. Mathematically, it can be expressed as: √x.y=√x×√y

To express the square root of 6 in the simplest form, we will make the number 6 as small as possible, ensuring to keep it as a whole number. Hence, the square root of 6 in simplest form is represented as√6=√2×√3. This can be further simplified by substituting the value of √2 and √3


\[\sqrt{6}=\sqrt{2}\times \sqrt{3}\]


\[\sqrt{6}=1.414\times 1.732\]


\[\sqrt{6}=2.449\]


Hence, the square root of 6 in simplest form is 2.449.  Similarly, we can also calculate the square root of any other whole numbers and their factors. Hence, simplifying the square root method is the simplest method of calculating the square root. We can also calculate the value of under root 6 using the calculator as this will give us the exact value. The exact value of the square root will always be given in a decimal number as it is impossible to determine a positive whole integer as a root for non-rational numbers.


Simplifying the Square Root Using Perfect Square Method

Following are the steps to simplify the square root using the perfect square method:


  1. Find the perfect square that divides the number in the radicand.

  2. Express the numbers as a factor of a perfect square.

  3. Simplify the radicals.


Solved Example

1. Simplify $\mathbf{\sqrt{300}}$

Solution:

\[\sqrt{300}=\sqrt{100\times 3}\]


\[\sqrt{300}=\sqrt{10\times 10\times 3}\]


\[\sqrt{300}=10\sqrt{3}\]


Hence,\[\sqrt{300}\] can be simplified as \[10\sqrt{3}\]


2. Simplify the following radical expressions :


  1. \[\sqrt{48}\]

  2. \[\sqrt{75}\]


Solutions:

i.$\mathbf{\sqrt{48}}$


Step 1: The perfect square 16 will divide the number 48.


Step 2: Express 48 as a factor of 16


48=16×3


Step 3: Reduce the square root of 16 as shown below:


\[\sqrt{48}=\sqrt{16\times 3}\]


\[\sqrt{48}=\sqrt{4\times 4\times 3}\]


\[\sqrt{48}=4\sqrt{3}\]


Hence,\[\sqrt{48}\] can be simplified as\[4\sqrt{3}\]


ii.$\mathbf{\sqrt{75}}$


Step 1: The perfect square 25 will divide the number 75.


Step 2: Express 75 as a factor of 25.


75=25×3


Step 3: Simplify the radicals as shown below: 


\[\sqrt{75}=\sqrt{25\times 3}\]


\[\sqrt{75}=\sqrt{5\times 5\times 3}\]


\[\sqrt{75}=5\sqrt{3}\]


Hence,\[\sqrt{75}\] can be simplified as\[5\sqrt{3}\]

FAQs on Square Root of 6

1. What is the Square Root of 6 in the Simplest Radical Form?

The square root of any number can only be simplified if the given number is divisible by a perfect square (other than number 1).√12 can be simplified further because 12 can be divisible by a perfect square i.e. 4. Similarly, √250 can also be simplified further because 250 can be easily divided by perfect square 25. But, √6 cannot be simplified further as 6 cannot be divided by a perfect square. Hence, the square root of 6 in the simplest radical form is expressed as √6.

2. Is the Value of Under Root 6 Rational or Irrational?

The value of under root 6 is considered as an irrational number because the number 6 is not a perfect square. This implies that the square root of 6 will have an infinite number when expressed in decimals. So, if we calculate the value of 6, we get the numbers that will go on into infinity, and will never repeat or terminate. It cannot be written even in the form of x/y, where y is not equal to 0. Hence, the value of 6  that we received is non-terminating.

3. How to Express the Value Under the Square Root 6 in a Fraction Form?

As we know, the value under the square root 6 is an irrational number. Therefore, the root 6 value cannot be expressed in an exact fraction form. However, we can make the value under the square root 6 into an approximate fraction by rounding it to the nearest hundredth. The square root of 6 to the nearest thousand is 2.45. Accordingly,

√6 = 2.45/1


= \[\frac{245}{100}\]


=\[\frac{2\times 9}{20}\]Hence, the approximate value of square root 6 in the fraction is 2 (9/20).

4. What is prime factorization?

To understand prime factorization, you need to know what is a factor and what are prime numbers. Take any number and try to find out the factors of that number for say 12 can be written as 1 × 12, 2 × 6, 3 × 4. So the factors are 1, 2, 3, 4, 6, and 12. And any number which is divisible by the number itself and 1. So, 2 and 3 are the prime factors of 12. And 12 can be written as 2×2×3. 

5.  How to find the square root of a number by the long division method?

Follow the steps given below to find the square root of a number by division method - 

  • Draw a line on the top of the number and a vertical line on the side of the number. 

  • Mark pairs of digits from the unit side till we cover the number completely

  • Look at the first pair from the left. For eg, if 8281 is your number then your first pair is 82

  • Find a perfect square that is equal to or lower than the first pair

  • Write the perfect square number on the left of the number

  • Then apply the multiply above and add the below method 

  • Subtract the perfect square from the first pair and write the result below

  • Bring down the next pair i,e 81 

  • Use the trial and error method to find out the perfect multiple of the remainder. 

  • In simple terms, you divide, multiply, subtract, bring down and repeat the steps. 

You can watch the video lecture on Vedantu’s website where we explain the concept using examples for easy understanding.