Question

$which \: is \: the \: following \: s \: an \: irrationall \: number \\ 0.3796 \\ 7.988478 \\ \\ \sqrt{225 } \\ \sqrt{23}$
answer of question​

Answer 1

${\underline {\boxed {\bf {\pink {\bigstar~Answer}}}}}$

We know that :-

• The rational numbers are the numbers that can be represented or show as the quotient or fraction of form p/q of two integers such that q is not equal to zero ( q ≠ 0 ) and this rational numbers are either terminating or repeating decimals.

• The irrational numbers are any real number that can not be represented or show as the quotient or fraction of form p/q of two integers such that q is not equal to zero ( q ≠ 0 ) and can be expressed as infinite decimal expansion with no repeating digit or group of digits.The decimal expansion of this numbers is non - terminating non - recurring .

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${\underline {\boxed {\bf {\red {\bigstar~Example \: = 1}}}}}$

${\underline {\boxed {\bf { {\bigstar~ \: 0.3796}}}}}$

Explanation :-

• The decimal expansion of this given number is terminating that is it is decimal number that contains a finite number of digits after the decimal point .

Therefore :-

${\underline {\boxed {\bf { {\bigstar~ \: 0.3796 \: is \: a \: rational \: number}}}}}$

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${\underline {\boxed {\bf {\red {\bigstar~Example \: = 3}}}}}$

${\underline {\boxed {\bf { {\bigstar~ \: \sqrt{225} }}}}}$

Explanation :-

$\rm \implies \: \sqrt{225} = 15 = \dfrac{15}{1} = \dfrac{p}{q}$

• The given number can be represented or show as the quotient or fraction of form p/q of two integers such that q is not equal to zero ( q ≠ 0 )

Therefore :-

${\underline {\boxed {\bf { {\bigstar~ \: \sqrt{225} \: is \: a \: rational \: number}}}}}$

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${\underline {\boxed {\bf {\red {\bigstar~Example \: = 4}}}}}$

${\underline {\boxed {\bf { {\bigstar~ \: \sqrt{23} }}}}}$

Explanation :

$\rm \implies \sqrt{23} = 4.79583152331..$

• The above number is also not perfect square number

• The decimal expansion of this numbers is non - terminating non - recurring and it can not be represented or show as the quotient or fraction of form p/q of two integers such that q is not equal to zero ( q ≠ 0 ) and can be expressed as infinite decimal expansion with no repeating digit or group of digits

Therefore :-

${\underline {\boxed {\bf { {\bigstar~ \: \sqrt{23} \: is \: a \: irrational \: number }}}}}$

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Answer 2

Step-by-step explanation:

$which \: is \: the \: following \: s \: an \: irrationall \: number \\ 0.3796 \\ 7.988478 \\ \\ \sqrt{225 } \\ \sqrt{23}$

answer of question