Question

classify the following number as rational or irrational : I. 3 + √ 2 II. √25 III. 2÷√5​

Answer 1

Question :

Classify the Following Numbers as Rational or Irrational :-

i. $\mathtt{3 + \sqrt 2}$

ii. $\mathtt{\sqrt {25}}$

iii. $\mathtt{\dfrac{2}{\sqrt 5}}$

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Solution :

i. $\mathtt{3 + \sqrt 2}$ is an Irrational Number since the Sum of a Rational and an Irrational Number is an Irrational Number.

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ii. $\mathtt{\sqrt{25} = 5}$, which is a Rational Number.

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iii. $\mathtt{\dfrac{2}{\sqrt 5}}$ is an Irrational Number since the Quotient of a Rational and an Irrational Number is an Irrational Number.

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Additional Information :

Irrational Numbers :-

A Number which can neither be expressed as a Terminating Decimal nor as a Repeating Decimal, is called an Irrational Number.

E.g. $\mathtt{0.01001000100001, \sqrt 2, \sqrt 5, \sqrt[3]{2}, \sqrt[3]{3}, \pi, etc... }$

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Rational Numbers :-

The Number of the form $\mathtt{\dfrac{p}{q}}$, where p and q are Integers and q ≠ 0, are known as Rational Numbers.

E.g. $\mathtt{\dfrac{1}{4}, \dfrac{3}{2}, \dfrac{11}{79}, -\dfrac{2001}{2002}, etc...}$

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If a is Rational and $\mathtt{\sqrt b}$ is Irrational, then each one of $\mathtt{(a + \sqrt b)}$, $\mathtt{(a - \sqrt b)}$, $\mathtt{a\sqrt b}$ and $\mathtt{\dfrac{a}{\sqrt b}}$ is Irrational.