Question

if √2 is irrational prove that 3+5√2 is irrational​

Answer 1

Step-by-step explanation:

please mark has brainliest answer

(❁´◡`❁)(✿ ♥‿♥)(❁´◡`❁)(✿ ♥‿♥)(❁´◡`❁)

Answer 2

Given :

√2 is Irrational number.

To prove :

3 + 5√2 is Irrational number.

Proof :

Let's us assume that 3 + 5√2 is a rational number .

Thus ,

3 + 5√2 = p/q , where p and q are integers and q ≠ 0 .

Now,

=> 3 + 5√2 = p/q

=> 5√2 = p/q - 3

=> 5√2 = (p - 3q)/q

=> √2 = (p - 3q)/5q -----(1)

If p/q is Rational then p/q - 3 is Rational.

If p/q - 3 is Rational then (p-3q)/q is Rational.

If (p-3q)/q is Rational then (p-3q)/5q is Rational.

If (p-3q)/5q is Rational then √2 is Rational.

{ using eq-(1) }

From eq-(1) , we get that √2 is Rational which contradicts the fact that √2 is an irrational number.

This, Our assumption is wrong and hence (3 + 5√2) is an irrational number.

Hence proved .