Question

prove that 4 minus 3 root 2 is an irrational number ​

Answer 1

Answer:

Let us assume, to the contrary that 4 - 5√2 is rational.

So, we can find coprime integers a and b(b ≠ 0) such that 4 - 5√2 = a/b => 5√2 = 4 - a/b

=> √2 = (4b - a)/5b

Since a and b are integers, (4b - a)/5b is rational.

So, √2 is rational.

But this contradicts the fact that √2 is irrational.

Hence, 4 - 5√2 is irrational.

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Answer 2

Step-by-step explanation:

let P upon Q is a rational number where (Q is not equal to zero) is equal to 4 - 3 root 2 .where p and q are coprime number .

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