1.

Prove 2-root 3 is irrational given that root 3 is irrational ​

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ANSWER:

Let's ASSUME that 2 - √3 is a RATIONAL number.

Square of the rational number is ALWAYS rational number.

But, (2 - √3)² = 5 - 4√3

Given: √3 is an irrational number.

But, when irrational number is added to a rational number it gives irrational number.

Hence, our ASSUMPTION goes wrong.

Therefore, 2 - √3 is an irrational number.



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