Question

Show that 3√2 is irrational.​

Answer 1

Step-by-step explanation:

Let us assume, to the contrary, that √3/2 is 

rational. Then, there exist co-prime positive integers a and b such that

√3/2=ba

⇒ 2=√3ba

⇒ 2 is rational       ...[∵√3,a and b are integers∴√3bais a rational number]

This contradicts the fact that 2 is irrational. 

So, our assumption is not correct.

Hence, √3/2 is an irrational number.

Answer 2

${\huge{\underline{\underline{\mathcal {\red{♡Question♡}}}}}}$

Show that 3√2 is irrational.

_____________________

${\huge{\underline{\underline{\mathcal {\red{♡Answer♡}}}}}}$

• Let 3√2 be a rational number

• A rational number can be written in the form of

p/q where p, q are integers.

3√2 = p/q

√2 = p/3q

p, q are integers then p/3q is a rational number.

Then √2 must be a rational number.

But this contradicts the fact that √2 is an irrational number.

♠ So, our supposition is false.

Therefore,

3√2 is an irrational number.

${\huge{\underline{\underline{\mathcal {\orange{♡Hence Proved♡}}}}}}$

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