Question

pls explain the answer... good answers will be marked as brainiest☆
4th question pls■​

Answer 1

Answer:

$\sf = \dfrac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15} }{- 19}$

Explanation:

Given fraction,

$\sf = \dfrac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{2} + 3 \sqrt{3} }$

We need to rationlise the denominator.

$\sf = \dfrac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{2} + 3 \sqrt{3} } \times \dfrac{2 \sqrt{2} - 3 \sqrt{3} }{2 \sqrt{2} - 3 \sqrt{3} }$

$\sf = \dfrac{(2 \sqrt{3} - \sqrt{5})(2 \sqrt{2} - 3 \sqrt{3}) }{(2 \sqrt{2} + 3 \sqrt{3})(2 \sqrt{2} - 3 \sqrt{3}) }$

$\sf = \dfrac{2 \sqrt{3}(2 \sqrt{2} - 3 \sqrt{3}) - \sqrt{5}(2 \sqrt{2} - 3 \sqrt{3}) }{(2\sqrt{2})^2 - (3\sqrt{3})^2}$

$\sf = \dfrac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15} }{8 - 27}$

$\sf = \dfrac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15} }{- 19}$

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Note:

Whenever we rationlise any rational number we need to multiply the number by its conjugate. Conjugate is formed by changing the sign between two terms in a binomial.

Answer 2

Step-by-step explanation:

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