Question

show that 3-2√5 is irrational
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Answer 1

Step-by-step explanation:

Given:-

3-2√5

To find:-

Show that 3-2√5 is an irrational number?

Solution:-

Let assume that

3-2√5 is a rational number

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

Let 3-2√5 = a/b

Where a and b are co-prime numbers

=> -2√5 = (a/b)-3

=> 2√5 = 3-(a/b)

=> 2√5 = (3b-a)/b

=> √5 = (3b-a)/2b

=> √5 is in the form of p/q

=> √5 is a rational number

But √5 is not a rational number.

It is an irrational number.

This contradicts to our assumption that is 3-2√5 is a rational number.

=> 3-2√5 is an irrational number.

Answer:-

3-2√5 is an irrational number.

Used method:-

• Method of Contradiction or Indirect method
• If q is a rational number and s is an irrational number then q+s,q-s,qs,q/s are also irrational numbers.