Question

Simplify

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

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{2} + 3 \sqrt{3} }$
On rationalizing the denominator we get,

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

Using the identity:

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$\frac{2 \sqrt{3}(2 \sqrt{2} + 3 \sqrt{3} ) - \sqrt{5}(2 \sqrt{2} - 3 \sqrt{3} ) }{ {(2 \sqrt{2}) }^{2} - {(3 \sqrt{3}) }^{2} } \\ \\ \\ = \frac{4 \sqrt{6} + 18 - 2 \sqrt{10} + 3 \sqrt{15} }{8 - 27 } \\ \\ \\ = \frac{18 + 4 \sqrt{6} - 2 \sqrt{10} + 3 \sqrt{15} }{19}$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺

Answer 2

See the attached Image :)

Hey!

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•Identity which is used :-

(a + b) (a - b)

= a² - b²

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Hope this is helpful for u :)

•Sorry for poor handwriting :(

Regards :)

Cybary

Be Brainly :)