Question

show tha 5-3√2 is irrational​

Answer 1

Answer:

We know that, 2 has non-terminating, non-repeating decimal expansion.

Hence it is an irrational number.

Using the properties of irrational numbers, we can say that the product of a non-zero rational number and an irrational number is always an irrational number.

Hence, 32 is an irrational number.

Further, we know that the difference of a rational number and an irrational number is always an irrational number.

Therefore, 5−32 is also an irrational number.