Question

Prove that (5+3root2) is an irrational number.​

Answer 1

Step-by-step explanation:

let 5+3√2 be rational number.

5+3√2=a/b

3√2=5-a/b

3√2=a-5b/b

√2. =a-5b/3b

here LHS is irrational where as s RHS is rational which can not be equal. Therefore our contradiction is wrong Therefore root 5 + 3 √2 is an irrational number..

Answer 2

ANSWER:

• 5+3√2 is an irrational number.

GIVEN:

• Number = 5+3√2

TO PROVE:

• (5+3√2) is an Irrational number.

SOLUTION:

Let (5+3√2) be a rational number which can be expressed in the form of p/q where p and q have no other Common factor than 1.

$\implies \: 5 + 3 \sqrt{2} = \dfrac{p}{q} \\ \\ \implies \: 3 \sqrt{2} = \dfrac{p}{q} - 5 \\ \\ \implies \: 3 \sqrt{2} = \dfrac{p - 5q}{q} \\ \\ \implies \: \sqrt{2} = \dfrac{p - 5q}{3q}$

Here:

• (p-5q)/3q is rational but √2 is Irrational.
• Thus our contradiction is wrong.
• 5+3√2 is an Irrational number.

Proved.