Math, asked by Salmonpanna2022, 1 month ago


\huge\tt\blue{question:-} \\  \\
 \sqrt{4 -  \sqrt{7} }  +  \sqrt{8 + 3 \sqrt{7} }  \: का \:  मान  \: कया \:  होगा \: । \\

Answers

Answered by shreyaSingh2022
4

Step-by-step explanation:

 \sqrt{4 -  \sqrt{7} }  +  \sqrt{8 + 3 \sqrt{7} }  \\  \\

 =  \sqrt{ \frac{(4 \sqrt{7}) \times 2 }{2} }  +  \sqrt{ \frac{(8 + 3 \sqrt{7} ) \times 2}{2} }  \\  \\

 =  \sqrt{ \frac{8 - 2 \sqrt{7} }{2} } +  \sqrt{ \frac{16 + 6 \sqrt{7} }{2} }   \\  \\

 =  \sqrt{ \frac{( \sqrt{7}  {) }^{2}  + 1 - 2 \sqrt{7} }{2} }  +  \sqrt{ \frac{(3 {)}^{2}  + ( \sqrt{7}  {)}^{2} + 2 \times 3 \times  \sqrt{7}  }{2} }  \\  \\

 =  \sqrt{ \frac{( \sqrt{7 } - 1 {)}^{2}  }{2} }  +  \sqrt{ \frac{(3 -  \sqrt{7} {)}^{2}  }{2} }  \\  \\

 =  \frac{ \sqrt{7}  - 1}{ \sqrt{2} }  +  \frac{3 \sqrt{7} }{ \sqrt{2} }  \\  \\

 =  \frac{ \sqrt{7 } - 1 + 3 +  \sqrt{7}  }{ \sqrt{2} }  \\  \\

 =  \frac{2 \sqrt{7}  + 2}{ \sqrt{2} } \\  \\

 =  \frac{ \sqrt{2} ( \sqrt{2}  \times  \sqrt{7} +  \sqrt{2}  }{ \sqrt{2} }  \\  \\

 =  \sqrt{2} ( \sqrt{7}  + 1) \\

Answered by Anonymous
0

Step-by-step explanation:

+

8+3

7

\begin{gathered} = \sqrt{ \frac{(4 \sqrt{7}) \times 2 }{2} } + \sqrt{ \frac{(8 + 3 \sqrt{7} ) \times 2}{2} } \\ \\ \end{gathered}

=

2

(4

7

)×2

+

2

(8+3

7

)×2

\begin{gathered} = \sqrt{ \frac{8 - 2 \sqrt{7} }{2} } + \sqrt{ \frac{16 + 6 \sqrt{7} }{2} } \\ \\ \end{gathered}

=

2

8−2

7

+

2

16+6

7

\begin{gathered} = \sqrt{ \frac{( \sqrt{7} {) }^{2} + 1 - 2 \sqrt{7} }{2} } + \sqrt{ \frac{(3 {)}^{2} + ( \sqrt{7} {)}^{2} + 2 \times 3 \times \sqrt{7} }{2} } \\ \\ \end{gathered}

=

2

(

7

)

2

+1−2

7

+

2

(3)

2

+(

7

)

2

+2×3×

7

\begin{gathered} = \sqrt{ \frac{( \sqrt{7 } - 1 {)}^{2} }{2} } + \sqrt{ \frac{(3 - \sqrt{7} {)}^{2} }{2} } \\ \\ \end{gathered}

=

2

(

7

−1)

2

+

2

(3−

7

)

2

\begin{gathered} = \frac{ \sqrt{7} - 1}{ \sqrt{2} } + \frac{3 \sqrt{7} }{ \sqrt{2} } \\ \\ \end{gathered}

=

2

7

−1

+

2

3

7

\begin{gathered} = \frac{ \sqrt{7 } - 1 + 3 + \sqrt{7} }{ \sqrt{2} } \\ \\ \end{gathered}

=

2

7

−1+3+

7

\begin{gathered} = \frac{2 \sqrt{7} + 2}{ \sqrt{2} } \\ \\ \end{gathered}

=

2

2

7

+2

\begin{gathered} = \frac{ \sqrt{2} ( \sqrt{2} \times \sqrt{7} + \sqrt{2} }{ \sqrt{2} } \\ \\ \end{gathered}

=

2

2

(

2

×

7

+

2

\begin{gathered} = \sqrt{2} ( \sqrt{7} + 1) \\ \end{gathered}

=

2

(

7

+1)

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