Rationalizing the denominator
2 root 3 - root 5 / 2 root 2 +3 root 3
Answers
Step-by-step explanation:
2√3 - √5/ 2√2 + 3 √3
= 2√3-{√5/2√2*-2√2/-2√2} +3√3
=2√3-{ -2√10/-4*2} +3√3
= 2√3-{√10/4} +3√3
= 2√3 - √10/4 + 3√3
=8√3 - √10 + 12√3/4
= 20√3 -√10/4
Answer:
We need to simplify the given expression :
\dfrac{2\sqrt{3}-\sqrt{5} }{2\sqrt{2}+3\sqrt{3} }
2
2
+3
3
2
3
−
5
Rationalizing both numerator and denominator, such that,
\dfrac{2\sqrt{3}-\sqrt{5} }{2\sqrt{2}+3\sqrt{3} }\times \dfrac{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
=\dfrac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{(2\sqrt{2})^2-(3\sqrt{3})^2 }=
(2
2
)
2
−(3
3
)
2
4
6
−18−2
10
+3
15
=\dfrac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{-19}=
−19
4
6
−18−2
10
+3
15
So, the value of \dfrac{2\sqrt{3}-\sqrt{5} }{2\sqrt{2}+3\sqrt{3} }
2
2
+3
3
2
3
−
5
is \dfrac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{-19}
−19
4
6
−18−2
10
+3
15
.
Learn more,
Simplification
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