Question

$\bf \:Find \: the \: value \: of \: { {((23 + {2}^{2}) }^{ \dfrac{2}{3} } + {(140 - 19)}^{ \dfrac{1}{2} } )}^{2}$​

Answer 1

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

$\sf \: { {((23 + {2}^{2}) }^{ \dfrac{2}{3} } + {(140 - 19)}^{ \dfrac{1}{2} } )}^{2}$

$\sf \: = { {((23 + 4) }^{ \dfrac{2}{3} } + {(121)}^{ \dfrac{1}{2} } )}^{2}$

$\sf:\implies \: {( {27}^{ \dfrac{2}{3} } + 11)}^{2}$

$\sf:\implies \: {(9 + 11)}^{2}$

$\sf:\implies \: {20}^{2}$

$\sf:\implies \:400$

$\sf:\implies \: \: the \: value \: is \: 400$

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Answer 2

Step-by-step explanation:

(23+2

2

)

3

2

+(140−19)

2

1

)

2

\begin{gathered}\sf \: = { {((23 + 4) }^{ \dfrac{2}{3} } + {(121)}^{ \dfrac{1}{2} } )}^{2} \\\\\end{gathered}

=((23+4)

3

2

+(121)

2

1

)

2

\begin{gathered}\sf:\implies \: {( {27}^{ \dfrac{2}{3} } + 11)}^{2}\\\\ \end{gathered}

:⟹(27

3

2

+11)

2

\begin{gathered}\sf:\implies \: {(9 + 11)}^{2} \\\\\end{gathered}

:⟹(9+11)

2

\begin{gathered}\sf:\implies \: {20}^{2} \\\\\end{gathered}

:⟹20

2

\begin{gathered}\sf:\implies \:400\\\\\end{gathered}

:⟹400