Question

(2sqrt(3) - sqrt(5))/(2sqrt(2) + 3sqrt(3))​

Answer 1

rhis is a your answer

ok..

Answer 2

Answer:

Required answer is $\frac{18 - 4 \sqrt{6} + 2 \sqrt{10} - 3 \sqrt{15} }{19}$

Step-by-step explanation:

Given,(2sqrt(3) - sqrt(5))/(2sqrt(2) + 3sqrt(3))

We can write,

$\frac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{2} + 3 \sqrt{3} }$

Here numerator is (3√3-√5) and denominator is (2√2+3√3)

We are multiplying numerator and denominator by (2√2-3√3) and get

$\frac{(2 \sqrt{3} - \sqrt{5} )(2 \sqrt{2} - 3 \sqrt{3} )}{(2 \sqrt{2} + 3 \sqrt{3} )(2 \sqrt{2} - 3 \sqrt{3} )}$

$= \frac{4 \sqrt{3 \times 2} - 6 \sqrt{3 \times 3} - 2 \sqrt{5 \times 2} + 3 \sqrt{5 \times 3} }{ {(2 \sqrt{2} )}^{2} - {(3 \sqrt{3}) }^{2} }$

$= \frac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15} }{8 - 27} \\ = \frac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15}}{ - 19} \\ = \frac{18 - 4 \sqrt{6} + 2 \sqrt{10} - 3 \sqrt{15} }{19}$

This is a problem of Power of indices.

Some important formulas of Power of indices :

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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