simplify the given expression under root 6 minus under root 2 under root 7 + under root 2
Answers
Step-by-step explanation:
Given expression is,
\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }
2
+
3
6
+
6
+
3
3
2
−
6
+
2
4
3
By rationalizing each term,
=\frac{\sqrt{6}(-\sqrt{2} + \sqrt{3}) }{(\sqrt{3})^2 - (\sqrt{2})^2 } + \frac{3\sqrt{2}(\sqrt{6}-\sqrt{3}) }{(\sqrt{6})^2-(\sqrt{3})^2 } - \frac{4\sqrt{3}(\sqrt{6}-\sqrt{2}) }{(\sqrt{6})^2-(\sqrt{2})^2 }=
(
3
)
2
−(
2
)
2
6
(−
2
+
3
)
+
(
6
)
2
−(
3
)
2
3
2
(
6
−
3
)
−
(
6
)
2
−(
2
)
2
4
3
(
6
−
2
)
=\sqrt{6}(-\sqrt{2} + \sqrt{3})+\sqrt{2}(\sqrt{6}-\sqrt{3} ) -\sqrt{3} (\sqrt{6}-\sqrt{2} )=
6
(−
2
+
3
)+
2
(
6
−
3
)−
3
(
6
−
2
)
=-\sqrt{12} + \sqrt{18} + \sqrt{12} - \sqrt{6} - \sqrt{18} + \sqrt{6}=−
12
+
18
+
12
−
6
−
18
+
6
=0=0
Hence,
\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }=0
2
+
3
6
+
6
+
3
3
2
−
6
+
2
4
3
=0. mark me brainest I. Given expression is,
\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }
2
+
3
6
+
6
+
3
3
2
−
6
+
2
4
3
By rationalizing each term,
=\frac{\sqrt{6}(-\sqrt{2} + \sqrt{3}) }{(\sqrt{3})^2 - (\sqrt{2})^2 } + \frac{3\sqrt{2}(\sqrt{6}-\sqrt{3}) }{(\sqrt{6})^2-(\sqrt{3})^2 } - \frac{4\sqrt{3}(\sqrt{6}-\sqrt{2}) }{(\sqrt{6})^2-(\sqrt{2})^2 }=
(
3
)
2
−(
2
)
2
6
(−
2
+
3
)
+
(
6
)
2
−(
3
)
2
3
2
(
6
−
3
)
−
(
6
)
2
−(
2
)
2
4
3
(
6
−
2
)
=\sqrt{6}(-\sqrt{2} + \sqrt{3})+\sqrt{2}(\sqrt{6}-\sqrt{3} ) -\sqrt{3} (\sqrt{6}-\sqrt{2} )=
6
(−
2
+
3
)+
2
(
6
−
3
)−
3
(
6
−
2
)
=-\sqrt{12} + \sqrt{18} + \sqrt{12} - \sqrt{6} - \sqrt{18} + \sqrt{6}=−
12
+
18
+
12
−
6
−
18
+
6
=0=0
Hence,
\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }=0
2
+
3
6
+
6
+
3
3
2
−
6
+
2
4
3
=0
Step-by-step explanation: