Question

which of following is irrattional √4/9,√7​

Answer 1

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Step-by-step explanation:

√7 will be the irrational

Answer 2

SOLUTION

TO DETERMINE

The irrational number

$\displaystyle \sf{ 1. \: \: \sqrt{ \frac{4}{9} } }$

$\displaystyle \sf{ 2. \: \: \sqrt{7} }$

CONCEPT TO BE IMPLEMENTED

RATIONAL NUMBER

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

Example

$\displaystyle \sf{2,- 1, \frac{1}{3} , - \frac{12}{23}} \: are \: the \: examples \: of \: rational \: numbers$

IRRATIONAL NUMBER

A number which is not rational is called irrational number

Example

√3 , π , e are irrational numbers

EVALUATION

Here the first number is

$\displaystyle \sf{ \sqrt{ \frac{4}{9} } }$

Which can be rewritten as

$\displaystyle \sf{ \sqrt{ \frac{4}{9} } = \frac{2}{3} }$

So the given number can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So the first number is rational

The second number is $\sf{ \sqrt{7} }$

The above number can not be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

Hence $\sf{ \sqrt{7} }$ is irrational number

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