Question

"The division of an irrational by another irrational number is always an irrational
number." Do you agree with this statement ? or not? support your answer with an
example.​

Answer 1

Answer:

this statement is not true !

Step-by-step explanation:

let's take 2 numbers a = 2√2 and b = √2

Now,

a/b = 2√2 / √2

a/b = 2

which is an integer !

Answer 2

The statement is not true

Step-by-step explanation:

Case 1:

Suppose two irrational numbers a=$2\sqrt 2, b=\sqrt 2$

Then, $\frac{a}{b}=\frac{2\sqrt 2}{\sqrt 2}$

$\frac{a}{b}=2$

We know that 2 is a rational number .

Therefore, we can say that when an irrational number is divided by another irrational number then the quotient is not a irrational number.

Hence, the statement is not true.

Case 2:$a=\sqrt 2, b=\sqrt 3$

$\frac{a}{b}=\frac{\sqrt 2}{\sqrt 3}$

It is an irrational number.

In this case the statement is true.

Therefore, the statement generally is not true.

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