Answers
Step-by-step explanation:
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)