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Answers
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Answer:
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Step-by-step explanation:
Since we have given that
\frac{4\sqrt{3}+5\sqrt{2}}{\sqrt{48}+\sqrt{18}}
48
+
18
4
3
+5
2
First we will rewrite √48 as 4√3.
And √18 as 3√2.
So, we will get that
\frac{4\sqrt{3}+5\sqrt{2} }{4\sqrt{3}+3\sqrt{2}}
4
3
+3
2
4
3
+5
2
Now, we will rationalize the denominator :
\begin{gathered}\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}\times \frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}}\\\\=\frac{48-12\sqrt{6}+20\sqrt{6}-30}{48-18}\\\\=\frac{18+8\sqrt{6}}{30}\\\\=\frac{9+4\sqrt{6}}{15}\end{gathered}
4
3
+3
2
4
3
+5
2
×
4
3
−3
2
4
3
−3
2
=
48−18
48−12
6
+20
6
−30
=
30
18+8
6
=
15
9+4
6
Hence, after rationalisation, we have
\frac{9+4\sqrt{6}}{15}
15
9+4
6