Question

Prove that 5-3√2 is irrational number given that√2 is irrational number

Answer 1

Answer:

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

Step-by-step explanation:

so. x = 5-3√2

x-5= - 3√2

x-5/-3 = √2

it is given that √2 is an irrational number... and we know that rational number ≠ an irrational number.. so our assumption is wrong 5-3√2 is an irrtional number.....

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Answer 2

Step-by-step explanation:

if 5-3√2 rational it is in the form of a/b.

5-3√2=a/b

- 3√2=(a/b)-5

3√2=5-(a/b)

3√2=(5b-a)/b

√2=(5b-a)/3b

given that √2 is irrational,but

(5b-a)/3b is rational.

But,we get

√2=(5b-a)/3b

so,our assumption is wrong.

5-3√2 is irrational.