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Mrac [35]
3 years ago
9

The sum or product of a non-zero rational number and an irrational number is always

Mathematics
2 answers:
vazorg [7]3 years ago
8 0
The product of a non-zero rational and an irrational number is always irrational (2)
frosja888 [35]3 years ago
8 0

Answer:

Option 2 - Irrational              

Step-by-step explanation:

To find :  The sum or product of a non-zero rational number and an irrational number is always  

Solution :

By the statement,

→ "The sum of a rational number and an irrational number is irrational."

Example : Let a rational number 3 and irrational number \sqrt{5}

Sum of rational and irrational number

3+\sqrt{5}= 3+2.236067977.....=5.236067977....

5.236067977.... is a irrational number as if you add a non-repeating and non-terminating decimal to a repeating decimal, you will have a repeating decimal.

→ "The product of a non-zero rational number and an irrational number is irrational."

Example : Let a rational number 3 and irrational number \sqrt{5}

Sum of rational and irrational number

3\times\sqrt{5}= 3\times2.236067977.....=6.708203931.....

6.708203931...... is a irrational number as If you multiply any irrational number by the rational number it gives you irrational except zero which is rational.

Therefore, Option 2 is correct.

The sum or product of a non-zero rational number and an irrational number is always  irrational.

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[

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