Question

Prove that √3 is an irrational number,Hence show that 5+√3 is also an irrational

Answer 1

Solution :

Let us assume , 5 + √3 is rational.

Let 5 + √3 = a/b , where a,b are

integers and b ≠ 0.

√3 = a/b - 5

=> √3 = ( a - 5b )/b

Since , a , b are integers , (a-5b)/b is

rational , and so √3 is rational .

This contradicts the fact that √3 is

irrational .

Hence , 5 + √3 is irrational.

••••••

Answer 2

Answer:

Step-by-step explanation:Solution :

Let us assume , 5 + √3 is rational.

Let 5 + √3 = a/b , where a,b are

integers and b ≠ 0.

√3 = a/b - 5

=> √3 = ( a - 5b )/b

Since , a , b are integers , (a-5b)/b is

rational , and so √3 is rational .

This contradicts the fact that √3 is

irrational .

Hence , 5 + √3 is irrational.