Properties of Irrational Numbers
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.
-x is a rational number
is a rational number.
x is a rational number
This contradicts the fact that x is irrational.
Hence, -x is an irrational number.
The decimal form of an irrational number is neither _______________ nor _________. | |||
| Right Option : A | |||
| View Explanation | |||
Does the square roots of all positive integers, irrational? | |||
| Right Option : A | |||
| View Explanation | |||
Is every irrational number, a real number? | |||
| Right Option : A | |||
| View Explanation | |||
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