If √3=1.732,then find the value of √27-3√75+5√48
Answers
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# ItzYourQueen01
Answer:
Heya user,
Here is the answer you were looking for:
\begin{gathered} \sqrt{27} - 3 \sqrt{75} + 5 \sqrt{48} + 2 \sqrt{108} \\ \end{gathered}
27
−3
75
+5
48
+2
108
On splitting we get,
\begin{gathered} \sqrt{3 \times 3 \times 3} - 3 \sqrt{5 \times 5 \times 3} + 4 \sqrt{2 \times 2 \times 2 \times 2 \times 3} + 2 \sqrt{2 \times 2 \times 3 \times 3 \times 3} \\ \\ = \sqrt{ {3}^{2} \times 3} - 3 \sqrt{ {5}^{2} \times 3 } + 4 \sqrt{ {2}^{2} \times {2}^{2} \times 3} + 2 \sqrt{ {2}^{2} \times {3}^{2} \times 3 } \\ \\ = 3 \sqrt{3} - 3 \times 5 \sqrt{3} + 4 \times 2 \times 2\sqrt{3} + 2 \times 2 \times 3 \sqrt{3} \\ \\ = 3 \sqrt{3} - 15 \sqrt{3} + 16 \sqrt{3} + 12 \sqrt{3} \\ \\ = 31 \sqrt{3} - 15 \sqrt{3} \\ \\ = 16 \sqrt{3} \\ \\ = 16 \times 1.732 \\ \\ = 27.712\end{gathered}
3×3×3
−3
5×5×3
+4
2×2×2×2×3
+2
2×2×3×3×3
=
3
2
×3
−3
5
2
×3
+4
2
2
×2
2
×3
+2
2
2
×3
2
×3
=3
3
−3×5
3
+4×2×2
3
+2×2×3
3
=3
3
−15
3
+16
3
+12
3
=31
3
−15
3
=16
3
=16×1.732
=27.712