Question

Write The Properties Of Irrational Numbers

Answer 1

Answer:

Step-by-step explanation:

Irrational numbers are real numbers that cannot be expressed as the ratio of two integers. More formally, they cannot be expressed in the form of p/q.

Properties of Irrational Numbers

Taking the sum of an irrational number and a rational number gives an irrational number. To see why this is true, suppose xx is irrational, yy is rational, and the sum x+yx+y is a rational number zz. Then we have x = z-yx=z−y, and since the difference of two rational numbers is rational, this implies xx is rational. This is a contradiction since xx is irrational. Therefore, the sum x+yx+y must be irrational.

Multiplying an irrational number with any nonzero rational number gives an irrational number. We argue as above to show that if xy = zxy=z is rational, then {x = \frac{z}{y}}x=  

y

z

​  

 is rational, contradicting the assumption that xx is irrational. Therefore, the product xyxy must be irrational.

The lowest common multiple (LCM) of two irrational numbers may or may not exist.

The sum or the product of two irrational numbers may be rational; for example,

\sqrt{2} \cdot \sqrt{2} = 2.

2

​  

⋅  

2

​  

=2.

Therefore, unlike the set of rational numbers, the set of irrational numbers is not closed under multiplication.

Answer 2

★ AnSwEr :

☬ Properties of irrational numbers are given below

• Irrational numbers can't be written in the form of p/q where p and q are integers.

• Irrational numbers can't be shown on number line.

• Irrational numbers have decimal expansions that neither terminate nor become periodic.

• If we add Irrational number rational number then our answer will be irrational number.

• Some examples of irrational numbers : √2, 22/7, √5 and many more.

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