Properties of Irrational Numbers


 
 
Concept Explanation
 

Properties of Irrational Numbers

Following are some useful results on irrational numbers, we state these results as theorems.

Theorem 1 Negative of an irrational number is an irrational number.

Proof:  Let x be an irrational number. Then, we have to show that -x is also an irrational number. If possible, let -x be a rational number.

We know that the negative of a rational number is also a rational number.

large therefore    -x is a rational number

large Rightarrow ;;-(-x) is a rational number.

large Rightarrow     x is a rational number

This contradicts the fact that x is irrational.

Hence, -x is an irrational number.

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Sample Questions
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Question : 1

The decimal form of an irrational number is neither _______________ nor _________.

Right Option : A
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Question : 2

Does the square roots of all positive integers, irrational?

Right Option : A
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Question : 3

Is every irrational number, a real number?

Right Option : A
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