Question

if x =3+√2 , check whether x+ 1 by X is rational number or irrational number​

Answer 1

Answer:

3+√2+1/3+√2

=4+√2/3+√2

Rationalize the denominator

Rationalizing factor= 3-√2

(4+√2)(3-√2)/ (3+√2)(3-√2)

=12-4√2+3√2-2/ ($3^{2}$)-(√$2^{2}$)

=10-√2/9-2

=10-√2/7

10-√2/7 is an irrational number.

Checking.

Lets Assume that 10-√2/7 is a rational number

10-√2/7= a/b, where a and b are co-prime integers.

10-√2= 7a/b

-(√2+10)= 7a/b

-√2=7a/b-10

-√2=7a-10b/b

Changing the negative sign of √2

√2= 10b-7a/b

Here, 10b-7a/b is a rational number, but this contradicts the fact that √2 is irrational.

Thus, Our Assumption is wrong, i.e.,  10-√2/7 is irrational

Step-by-step explanation: