Question

show that (4plus3√2) is irrational​

Answer 1

Answer:

$\huge\color{blue}\boxed{\colorbox{black}{♡Answer:-♡}}$

Let 4+3√2

be a rational number. 

Then both 4+3√2 and 4 are rational. 

⇒ 4+3√2 – 4 = 3√2 = rational

[∵Difference of two rational numbers is rational] ⇒ 3√2 is rational. 

⇒ 1/3 3√2 is rational.

[∵ Product of two rational numbers is rational] ⇒ √2 is rational. 

This contradicts the fact that √2 is irrational when 2 is prime √2 is irrational 

Hence 4 + 3√2 is irrational.

Hope it help uh ✌

Answer 2

Step-by-step explanation:

be a rational number.

Then both 4+3√2 and 4 are rational.

⇒ 4+3√2 – 4 = 3√2 = rational

[∵Difference of two rational numbers is rational]

⇒ 3√2 is rational. ⇒ 1/3 3√2 is rational.[∵ Product of two rational numbers is rational]

⇒ √2 is rational.

This contradicts the fact that √2 is

irrational when 2 is prime √2 is irrational Hence 4 + 3√2 is irrational.

Hope it help uh ✌