Question

loga^3 =2 why a is irrational give reason​

Answer 1

Because there is no rational power to which you can raise 3 and get 2

Answer 2

a is irrational, it can not be written as $\dfrac{p}{q}$ form, where q ≠ 0.

Step-by-step explanation:

We have,

$\log_a3$ = 2

Give region, why 'a' is irrational ?

∴ $\log_a3$ = 2

Using the properties of logarithm,  

⇒ $a^2$ = 3

⇒ a = $3^{\dfrac{1}{2}}$

⇒ a = $\sqrt{3}$

⇒ a = 1.73220508......

It can not be written as $\dfrac{p}{q}$ form, where q ≠ 0.

∴ a is irrational.