Math, asked by hadleyjose3105, 2 months ago

Simplify each of the following by rationalizing the denominator 2 √3 - √5 / 2 √2 + 3 √3​

Answers

Answered by Anonymous
8

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

Answered by Anonymous
2

Answer:

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