Question

prove that 2 root 3 - 4 is an irrational number​

Answer 1

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Answer 2

Step-by-step explanation:

Given :-

2√3-4

To find :-

Prove that 2√3-4 is an irrational number?

Solution :-

Let us assume that 2√3-4 is a rational number

=> It must be in the form of p/q ,where p and q are integers and q≠0

Let 2√3-4 = a/b ( a,b are co -primes)

=> 2√3 = (a/b)+4

=> 2√3 = (a+4b)/b

=> √3 = (a+4b)/2b

=> √3 is in the form of p/q

=> √3 is a rational number.

But √3 is not a rational number.

√3 is an irrational number.

This contradicts to our assumption that is 2√3-4 is a rational number.

So, 2√3-4 is an irrational number.

Hence , Proved.

Answer:-

2√3-4 is an irrational number.

Used Method:-

• Method of Contradiction or Indirect method

Points to know :-

• The numbers are in the form of p/q,where p and q are integers and q≠0 called rational numbers and they are denoted by Q.

• The numbers are not in the form of p/q,where p and q are integers and q≠0 called irrational numbers and they are denoted by Q' or S.

• If q is a rational number and s is an irrational number then

1. q+s is an irrational number.
2. q-s is an irrational number.
3. q×s is an irrational number.
4. q/s is an irrational number.