Given that root 2 is irrational, prove that (5+3 root3) is an irration

1.	Given that root 2 is irrational, prove that (5+3 root3) is an irrational number.
Answer» Given that, √2 is irrational To prove: 5 + 3√2 is irrational Assumption: Let us assume 5 + 3√2 is rational. Proof: As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and p & q are co prime. Then, 5+3√2=p/q3√2=p/q-5hence√2=p-5q/3qWe know √2 is irrationalp-5q/3q is rationalrational is not equal to irrationalhence5+3√2 is irrational

Given that root 2 is irrational, prove that (5+3 root3) is an irrational number.

Answer»

Given that,

√2 is irrational

To prove:

5 + 3√2 is irrational

Assumption:

Let us assume 5 + 3√2 is rational.

Proof:

As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and p & q are co prime.

Then,

5+3√2=p/q3√2=p/q-5hence√2=p-5q/3qWe know √2 is irrationalp-5q/3q is rationalrational is not equal to irrationalhence5+3√2 is irrational