Prove That 4 − 5√2 Is an Irrational Number

Video Explanation

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

Solution

Question: Prove that 4 − 5√2 is an irrational number.

Proof:

Let us assume that 4 − 5√2 is a rational number.

Since 4 is a rational number, subtracting 4 from both sides, we get:

−5√2 = (4 − 5√2) − 4

This implies that −5√2 is a rational number.

Dividing both sides by −5 (which is a non-zero rational number), we get:

√2 is a rational number.

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

∴ Our assumption is wrong.

Hence, 4 − 5√2 is an irrational number.

Final Answer

∴ 4 − 5√2 is an irrational number.

Conclusion

Thus, by the method of contradiction (as per NCERT Class 10), we have proved that 4 − 5√2 is irrational.