Prove That 2√3 − 1 Is an Irrational Number

Video Explanation

Watch the video below for the complete NCERT-based explanation:

Solution

Question: Prove that 2√3 − 1 is an irrational number.

Proof:

Let us assume that 2√3 − 1 is a rational number.

Since 1 is a rational number, adding 1 to both sides, we get:

2√3 = (2√3 − 1) + 1

This implies that 2√3 is a rational number.

Dividing both sides by 2 (which is a non-zero rational number), we get:

√3 is a rational number.

But this is a contradiction because √3 is an irrational number.

∴ Our assumption is wrong.

Hence, 2√3 − 1 is an irrational number.

Final Answer

∴ 2√3 − 1 is an irrational number.

Conclusion

Thus, by the method of contradiction, we have proved that 2√3 − 1 is irrational.