simplify 6/2√3+√6 + √6/√3+√2 - 4√3/√6√2
Answers
Answer:
Answer - 0
Step-by-step explanation:
Here, the given expression is,
\frac{6}{2\sqrt{3}-\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}
2
3
−
6
6
+
3
+
2
6
−
6
−
2
4
3
By rationalizing,
=\frac{6}{2\sqrt{3}-\sqrt{6}}\times \frac{2\sqrt{3}+\sqrt{6}}{2\sqrt{3}+\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}\times \frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}}=
2
3
−
6
6
×
2
3
+
6
2
3
+
6
+
3
+
2
6
×
3
−
2
3
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2
−
6
−
2
4
3
×
6
+
2
6
+
2
=\frac{6(2\sqrt{3}+\sqrt{6})}{6}+\frac{\sqrt{6}(\sqrt{3}-\sqrt{2})}{1}-\frac{4\sqrt{3}(\sqrt{6}+\sqrt{2})}{4}=
6
6(2
3
+
6
)
+
1
6
(
3
−
2
)
−
4
4
3
(
6
+
2
)
( (a+b)(a-b) = a² - b² )
=2\sqrt{3}+\sqrt{6}+\sqrt{6}(\sqrt{3}-\sqrt{2})-\sqrt{3}(\sqrt{6}+\sqrt{2})=2
3
+
6
+
6
(
3
−
2
)−
3
(
6
+
2
)
=2\sqrt{3}+\sqrt{6}+\sqrt{18}-\sqrt{12}-\sqrt{18}-\sqrt{6}=2
3
+
6
+
18
−
12
−
18
−
6
=2\sqrt{3}+\sqrt{6}+3\sqrt{2}-2\sqrt{3}-3\sqrt{2}-\sqrt{6}=2
3
+
6
+3
2
−2
3
−3
2
−
6
( Because, √18 = √(9×2) = √9 × √2 = 3√2 and √12 = √(4×3) = √4 × √3 = 2√3 )
=0=0
Step-by-step explanation:
6 √6. 4√3
------. + √6 + ----------- - ----------
2√3. √3+√2. √6√2
6×√3. √6(√3-√2). 4√3
-------------. + √6. + -----------------------. - ------------
2×√3×√3. (√3+√2)(√3-√2). √3√2√2
√3 +√6 + √6(√3-√2) - 2
√3+√6 + √18 - √12 -2
√3+ √6 + 3√2 - 2√3 - 2
√6 + 3√2 - √3 -2