Question

Insert two irrational numbers between root 3 and root 6

Answer 1

Two irrational number between √3 and √6 is √3.1 and √5

GIVEN

Irrational numbers- √3 and √6

TO FIND

Two find two irrational numbers between the given numbers.

SOLUTION

We can simply solve the above problem as follows;

We know that irrational numbers are those numbers that cannot be written in the form of a/b. That is, it cannot be written in the form of simple fractions.

We are given two irrational numbers- √3 and √6.

We know that,

√3 < √4 < √5< √6

Since,

√4 = 2

Therefore, √4 is not an irrational number.

Other rational number can be = √3 × √0.1 = √3.1 is an irrational number.

Hence, Two irrational number between √3 and √6 is √3.1 and √5

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Answer 2

The answer is 1.74, 1.75, 1.76, 1.77 .....etc

Given :

Numbers √3 and √4

To find:

Two irrational numbers between √3 and √6

Solution:

Irrational Number

• An irrational number is number which cannot be written in the form of simple fractions or in the form of p/q.

• These numbers could be in the form of decimals but not as fractions

     Example :

• π is an irrational number since the value of  π = 3.142… is never ending value

• √2, 0.89, 2.59888, 0.3 ...etc.  

Given numbers √3 and √6

Here  √3 = 1.7320  and √6 = 2.44948  

⇒ The irrational numbers between √3 and √6  will be

1.743, 1.75, 1.756, 1.757, 1.76.....   like this we can insert infinite numbers between two irrational numbers  

The answer is 1.74, 1.75, 1.76, 1.77 .....etc

 

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