Question

prove that 3 - 3 root under 2 is a rational number​

Answer 1

Step-by-step explanation:

3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. But this contradicts the fact that √2 is irrational.. So, it concludes that 3+√2 is irrational..

Answer 2

Answer:

case 1

let us assume √2 is a rational number

√2=a\b where a and b are co- prime non negative integers

√2b = a. 1

squaring both the sides

(√2b)^2 = (a)^2

2b^2 = a^2

b^2 = a^2/2

therefore 2 is the common factor of a^2 and a a= 2c where c is some integer

equation 1 implies

√2b =a

squaring both the sides

2b^2 = 4c^2

b^2 = 2c^2

b^2/2 = c^2

therefore 2 is a common factor of b^2 and b

this controdict the fact that √2 is rational since 2 is a common factor of a and b

case 2

let us assume 3-3√2 is rational

3-3√2 = a/b where a and b are co- prime non negative integers

-3√2 = a/b -3

-3√2= a-3b/b

√2 = a-3b/b/-3

√2 = -3a+9b/b

√2 is irrational and -3a+9b/b is rational

so 3-3√2 is irrational