Show That 5 − 2√3 Is an Irrational Number

Video Explanation

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

Solution

Question: Show that 5 − 2√3 is an irrational number.

Proof:

Let us assume that 5 − 2√3 is a rational number.

Since 5 is a rational number, subtracting 5 from both sides, we get:

−2√3 = (5 − 2√3) − 5

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, 5 − 2√3 is an irrational number.

Final Answer

∴ 5 − 2√3 is an irrational number.

Conclusion

Thus, by the method of contradiction (as per NCERT Class 10), we have proved that 5 − 2√3 is irrational.