Question

Prove that 1 by root 3 is irrational

Answer 1

Let as assume to the contrary that 1/✓3 is rational number

1/✓3= P/Q { where p and Q are co-prime and Q not equal to 0}

✓3 P =Q .1

✓3 = Q/P

✓3 = Irrational number

Q/P =Rational

Irrational not equal to rational

this is a contradiction has arisen by the wrong assumption because of our incorrect assumption that 1 / ✓3 is rational.

hence, 1/ ✓3 is irrational .{proved}

Answer 2

Answer:

Step-by-step explanation:

Hii friend,

We have 1/✓3 = 1/✓3 × ✓3/✓3 = 1/3 × ✓3.... (1)

If possible, Let 1/✓3 be rational Number. Then , from (1) , 1/3×✓3 is rational Number.

Now, 3 is rational , 1/3×✓3 is rational.

=> 3 × 1/3 × ✓3 is also rational. [ Because product of two rationals is rational]

=> ✓3 is rational.

This contradicts the fact that ✓3 is irrational.

Since,

The contradiction arises by assuming that 1/✓3 is rational. So, 1/✓3 is irrational..... PROVED.......

HOPE IT WILL HELP YOU...... :-)