Question

Show that following are irrational numbers: (I)2−√3 (II)3+√2 (III)5−2√3​

Answer 1

Answer:

Step-by-step explanation:

(I) 2 - √3

now let's assume that this is rational number

then it can be expressed as a/b where a and b are co primes.

2- √3 = a/b

- √3 = a/b - 2

√3 = 2 - a/b

but we know, √3 is irrational

but our assumption was 2 - √3 should also be rational.

The contradiction had arisen due our incorrect assumption, that 2 - √3 is rational.

therefore, 2 - √3 is irrational

And the statements would remain same for other questions

just transpose all number to RHS and leave the number is root in LHS

hope this helps ☺️