Question

if r is rational and s is irrational,which statement is false?a) r+s irrational number.b) r-s irrational.c)rs irrational.d)r/s irrational number.
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Answer 1

Step-by-step explanation:

Since S is not a rational number, then the initial premise that “R+S and R are rational numbers” is not true. So, if R is a rational number, then R+S cannot be a rational number when S is an irrational number.

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Answer 2

Given that:

r is rational and s is irrational.

To find:

false statement among (sum or product or difference or quotient ) of r and s.

Solution:

For given r and s , the statement (c)rs irrational and (d) r/s irrational both can be false as it depends on the value of irrational number that the rational number gives rational or irrational as a result on dividing and multiplying by a non zero irrational number.

There are exceptions too:

For example, let r be 2(rational) and s(irrational) be √4,

on multiplying r×s ,we get

= 2 × 2 [value of √4 is 2]

=4 (rational number)

Now, taking r=3 and s= √9,

on dividing r/s we get,

=3÷√9 [ as value of √9 is 3]

=3÷3

=1 (rational number)

So, the correct option for the above question could be (d) r/s is irrational number or (c) r×s is irrational except the exception.

{ For the rest, addition of a rational number and an irrational number is always an irrational number.

And, subtraction of a irrational number from a rational or rational number from irrational number is always an irrational number.}