State true or false: Product of two irrational number is always irrational.

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True

False

answer is B.

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Detailed Solution

The given statement is that the product of two irrational number is always irrational.
Here, we have to state if the given statement is true or not.
It is the property of irrational numbers that they are not closed under multiplication, i.e., multiplying two or more irrational numbers may give the product as either rational or irrational.
For example:

2 × 5 = 2 × 5 = 10

, which is irrational.

22 × 22 = 4 2 × 2 = 8

, which is rational.
Hence, the given statement is false.
Product of two irrational numbers can be rational or irrational.
So, the correct option is 2.

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