Question

Show that (3-2root5) is an irrational number

Answer 1

Answer:

suppos 3-2√5 is a rational no. that ca be expressed in the form of p/q

3-2√5=p/q

. √5=p/2q -3/2

p/2q -3/q is a rational no.

i.e. √5 is also a rational no.

This is not possible because it is in the form of p/q

This is contradiction

Our supposition is wrong

i.e 3-2√5 is an irrational no.

Hope it helps you

Answer 2

Solution:

Let us assume (3-2√5) is a

rational number.

3-2√5 = a/b

where a,b are integers, b≠0

=> 3-a/b = 2√5

=> (3b-a)/b = 2√5

=> (3b-a)/2b = √5

Since , a,b are integers, (3b-a)/2b is a rational,so, √5 is rational.

But , It contradicts the fact that

√5 is an irrational.

Therefore,

3-2√5 is an irrational number.

••••