[tex]\large\underline{\sf{Solution-}}[/tex]
Given rational numbers are 0.77 and 0.78
Now, we have to find two different irrational numbers between 0.77 and 0.78.
Let's first recall the definition of irrational number.
Irrational number are those numbers whom decimal representation is neither terminating nor repeating.
So, two different irrational numbers between 0.77 and 0.78 are
[tex]\sf \: 0.77077007700077... \\ \\ [/tex]
[tex]\sf \: 0.77078007800078... \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional information :-
Rational number are those numbers whom decimal representation is either terminating or non terminating but repeating.
If a and b are two real numbers, then a rational number between a and b is [tex]\dfrac{a+b}{2} [/tex].
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]
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Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
Given rational numbers are 0.77 and 0.78
Now, we have to find two different irrational numbers between 0.77 and 0.78.
Let's first recall the definition of irrational number.
Irrational number are those numbers whom decimal representation is neither terminating nor repeating.
So, two different irrational numbers between 0.77 and 0.78 are
[tex]\sf \: 0.77077007700077... \\ \\ [/tex]
[tex]\sf \: 0.77078007800078... \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional information :-
Rational number are those numbers whom decimal representation is either terminating or non terminating but repeating.
If a and b are two real numbers, then a rational number between a and b is [tex]\dfrac{a+b}{2} [/tex].
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]