Question

Prove that 4-5root 2 is an irrational number​

Answer 1

Question: Prove that 4-5root 2 is an irrational number.

Solution :

Let us assume that 4-5√2 is be rational.

=> 4-5√2 = a/b [ where, a,b belongs to Z]

=> -5√2 = a/b -4

=> √2 = 4/5 -a/b

L.H.S = irrational number as √2 is an irrational number .

R.H.S = rational number

Hence, R.H.S ≠ L.H.S

Therefore, our assumption is wrong & 4-5√2 is an irrational number.

Hence, (proved)

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