CBSE BOARD X, asked by dalbhaat, 1 year ago

Prove that 1/3+√3 is irrational​

Answers

Answered by paneer1077
0
sum of rational and an irrational number is is always irrational
Answered by AnushkaSahoo
2

Answer:

Let us assume that 1/3+sqrt3 is a rational number.

=> 1/3+sqrt 3=a where 'a' is a rational number

=> sqrt3= a-1/3

Here 'a' is a rational number and we know that 1/3 is also a rational number.

=> a-1/3 is also a rational number.

=> sqrt3 is a rational number.

But it contradicts the fact that root 3 is an irrational number.

Thus, our assumption is wrong.

Therefore 1/3+sqrt3 is an irrational number.

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