Simplify each of the following by rationalizing the denominator 2 √3 - √5 / 2 √2 + 3 √3
Answers
Answer:
Answer:
\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}=\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19}
2
2
+3
3
2
3
−
5
=
19
18−4
6
+2
10
−3
15
Step-by-step explanation:
Consider,
\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}
2
2
+3
3
2
3
−
5
We multiply and divide by 2√2 - 3√3
we get,
\implies\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}\times\frac{2\sqrt{2}-3\sqrt{3}}{2\sqrt{2}-3\sqrt{3}}⟹
2
2
+3
3
2
3
−
5
×
2
2
−3
3
2
2
−3
3
\implies\frac{(2\sqrt{3}-\sqrt{5})(2\sqrt{2}-3\sqrt{3})}{(2\sqrt{2}+3\sqrt{3})(2\sqrt{2}-3\sqrt{3})}⟹
(2
2
+3
3
)(2
2
−3
3
)
(2
3
−
5
)(2
2
−3
3
)
\implies\frac{4\sqrt{6}-6\times3-2\sqrt{10}+3\sqrt{15}}{(2\sqrt{2})^2-(3\sqrt{3})^2}⟹
(2
2
)
2
−(3
3
)
2
4
6
−6×3−2
10
+3
15
\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{8-27}⟹
8−27
4
6
−18−2
10
+3
15
\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{-19}⟹
−19
4
6
−18−2
10
+3
15
\implies\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19}⟹
19
18−4
6
+2
10
−3
15
Answer:
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