Question

1÷√3 is it rational or irrational?​

Answer 1

Answer:

1 / $\sqrt{3}$ is an irrational number

Step-by-step explanation:

Since value of $\sqrt{3}$ does not have accurate/pure value. Therefore, the division will also give us an irrational number.

Answer 2

Answer:

$\huge\frak\red{❒Answer}$

No,

❒Suppose 1/√︎3 = a/b for coprime a,b:

1/3 = a²/b²

b² = 3a²

⟼We observe that 3|b² and this implies 3|b or equivalenty that 3²|b², since 3 is prime.

∴So there exists a c such that b² = 9c

9c = 3a² ⇒︎ 3c = a², we go through a similar arguement to say 3|a.

⟼And we have a contradiction to a and b coprime.

⟼Any rational number can be written as a reduced fraction where the GCD of top and bottom is one,

• We show we can never arrive there.

1/√︎3 is irrational