VALUE OF ROOT 6: Methods With Explanation – MINDSPARK.

What is the value of root 6?

The root value of a number means the square root of a number i.e a number with the power of half. The root value of a number x can be represented as x^{1 / 2} \text { or } x^{0.5} \text { or } \sqrt{x}. Therefore root value of 6 can be represented in three forms :

1. Root Value of 6: 2.4494897 or we can write it just using 3 decimal places = 2.449.

2. Root value of 6 in exponential form: 6^{1 / 2} \text { or } 6^{0.5}.

3. Root value of 6 in radical form: \sqrt{6}.

How to find the value of root 6?

We can find the value of root 6 by 2 methods:

1. Prime Factorisation: In this method first we write the numbers using the prime factors, take the root of them and put the value of the roots of the prime factors. We can find the value of root 6 by doing the following steps

\sqrt{6}=\sqrt{2 \times 3}
\Rightarrow \sqrt{6}=\sqrt{2} \times \sqrt{3}

Now we know the value of \sqrt{2}=1.414 \text { and } \sqrt{3}=1.732

\Rightarrow \sqrt{6}=1.414 \times 1.732
\Rightarrow \sqrt{6}=2.449

2. Long Division: In this method, we write the number of which we have to find the root (here we will write 6) in the form of pairs as shown in the image below.

⇒ Now take the number whose square is less than 6. We know 2^{2}=4which is less than 6. Now place 2 where the divisor should be and divide it by 6 normally as we do in the long division method. After dividing we get 2 at the place of quotient and 2 as the remainder. We write the remainder.

 ⇒ Now we’ll use the pairs of zeros to continue with this method. On Bringing down the pair of zero, we’ll get 200 as the dividend. Add 2 to itself which will give us 4 which will become the starting digit of our divisor. Now we have 4y as a divisor and we have to put such a value of y so that 4y × y is less than 200. Therefore only number 4 is appropriate to be put in the place of y. Now with 44 as the divisor and 200 as the dividend, we will do normal division. We will get 4 at the place of quotient and 24 as the remainder.

 ⇒ Repeat the steps given above we will find the value of root 6.

Value of root 6 = 2.449

Examples:

1. What will be the value of \sqrt{6}+\sqrt{6}?

Since the value of the under roots is the same, we will add them normally.

\sqrt{6}+\sqrt{6}=2 \sqrt{6} 

2. What will be the value of \sqrt{6} \times \sqrt{6} ?

\sqrt{6} \times \sqrt{6}=6^{1 / 2} \times 6^{1 / 2}=6^{0.5+0.5}=6^{1}=6

3. Is root 6 an irrational number?

A number is said to be a rational number when it can be written in a form of a/b, where a and b are integers and b ≠ 0. Root 6 on the other hand cannot be written in the form of  a/b. Therefore root 6 is an irrational number.