Show That 3 + √2 Is an Irrational Number

Video Explanation

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

Solution

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

Proof:

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

Since 3 is a rational number, subtracting 3 from both sides, we get:

√2 = (3 + √2) − 3

This implies that √2 is a rational number.

But this is a contradiction because √2 is an irrational number.

∴ Our assumption is wrong.

Hence, 3 + √2 is an irrational number.

Final Answer

∴ 3 + √2 is an irrational number.

Conclusion

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