rationalise the denominator of (i) (5/2+√2) (ii) (2√3+5)
Answers
Answer:
The given expression is
\frac{3}{\sqrt{3}+\sqrt{5}-\sqrt{2}}
3
+
5
−
2
3
Rationalize the denominator.
\frac{3}{(\sqrt{3}+\sqrt{5})-\sqrt{2}}\times \frac{(\sqrt{3}+\sqrt{5})+\sqrt{2}}{(\sqrt{3}+\sqrt{5})+\sqrt{2}}
(
3
+
5
)−
2
3
×
(
3
+
5
)+
2
(
3
+
5
)+
2
\frac{3(\sqrt{3}+\sqrt{5})+3\sqrt{2}}{(\sqrt{3}+\sqrt{5})^2-(\sqrt{2})^2}
(
3
+
5
)
2
−(
2
)
2
3(
3
+
5
)+3
2
\frac{3\sqrt{3}+3\sqrt{5}+3\sqrt{2}}{3+5+2\sqrt{15}-2}
3+5+2
15
−2
3
3
+3
5
+3
2
\frac{3\sqrt{3}+3\sqrt{5}+3\sqrt{2}}{6+2\sqrt{15}}
6+2
15
3
3
+3
5
+3
2
Rationalize the denominator.
\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})}{6+2\sqrt{15}}\times \frac{6-2\sqrt{15}}{6-2\sqrt{15}}
6+2
15
3(
3
+
5
+
2
)
×
6−2
15
6−2
15
\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{6^2-(2\sqrt{15})^2}
6
2
−(2
15
)
2
3(
3
+
5
+
2
)(6−2
15
)
\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{36-60}
36−60
3(
3
+
5
+
2
)(6−2
15
)
\frac{3(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{-24}
−24
3(
3
+
5
+
2
)(6−2
15
)
-\frac{(\sqrt{3}+\sqrt{5}+\sqrt{2})(6-2\sqrt{15})}{8}−
8
(
3
+
5
+
2
)(6−2
15
please mark in brainlist
)
\frac{\sqrt{3}}{2}-\frac{3\sqrt{2}}{4}+\frac{\sqrt{30}}{4}
2
3
−
4
3
2
+
4
30
Therefore the simplified form is \frac{\sqrt{3}}{2}-\frac{3\sqrt{2}}{4}+\frac{\sqrt{30}}{4}
2
3
−
4
3
2
+
4
30
Step-by-step explanation:
1)