Question

given that under root 2 is irrational,prove that (5+3under root 2) is an irrational number

Answer 1

Hii friend,



✓2 is irrational ( given)

To prove :- 5+3✓2 is irrational.

Let 5+3✓2 is irrational Number . 5 is rational.

(5+3✓2) -5

3✓2 is rational. [ Difference of rational and rational is rational.]

1/3×3✓2 = ✓2 is rational. [ product of rational and rational is rational].

But ✓2 is irrational. ( given).

So ,

The contradicts the fact that ✓2 is irrational.

Thus,

The contradiction arises by assuming that 5+3✓2 is rational.

Hence,

5+3✓2 is irrational. ... PROVED....


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