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The Product of Two Irrational Numbers is an Irrational Number (True/False). - Mathematics

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Question

The product of two irrational numbers is an irrational number (True/False).

Numerical

Solution

The product of two irrational numbers is an irrational number (True/False)

False

Reason:

Let us assume the two irrational numbers be `sqrt2` and `sqrt3`

Sometimes, it is and sometimes it isn't. 

`sqrt2` And  `sqrt3` are both irrational as their product is `sqrt6`

Now `sqrt2` and `sqrt8` are both irrational but their product, `sqrt16 ` is rational (in fact, it equals 4)

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Chapter 1: Real Numbers - Exercise 1.7 [Page 58]

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RD Sharma Mathematics [English] Class 10
Chapter 1 Real Numbers
Exercise 1.7 | Q 27 | Page 58

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