Answer:
Here is your answer,
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Q. If the √2 = 1.414 , √5 = 2.236 and √3 = 1.732 ,find the value of -
\begin{gathered}(1) \: \: \sqrt{72} + \sqrt{48} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ \\ 6 \sqrt{2} + 4 \sqrt{3} \\ \\ 6 \times 1.414 + 4 \times 1.732 \\ \\ 8.484 + 6.928 \\ \\ 15.412\end{gathered}
(1)
72
+
48
2×2×2×3×3
+
2×2×2×2×3
6
2
+4
3
6×1.414+4×1.732
8.484+6.928
15.412
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\begin{gathered}(2) \: \: \sqrt{ \frac{125}{64} } \\ \\ \frac{ \sqrt{125} }{ \sqrt{64} } \\ \\ \frac{ \sqrt{5 \times 5 \times 5} }{ \sqrt{8 \times 8} } \\ \\ \frac{5 \sqrt{5} }{8} \\ \\ \frac{5 \times 2.236}{8} \\ \\ \frac{11.180}{8} \\ \\ 1.3975\end{gathered}
(2)
64
125
64
125
8×8
5×5×5
8
5
5
8
5×2.236
8
11.180
1.3975
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Hence,
\begin{gathered}(1) \: \: \sqrt{72} + \sqrt{48} = 15.412 \\ \\ (2) \: \: \sqrt{ \frac{125}{64} } = 1.3975\end{gathered}
(1)
72
+
48
=15.412
(2)
64
125
=1.3975
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Hope it helps.