Question

EVALUATE :-

[(15)/(√10+√20+√40+√5- √80)]

give the answer by ur own ! no copy paste from other answers. The answer should be with steps.

SPAMMERS STAY AS FAR AS POSSIBLE OE ELSE THE CONSEQUENCES WONT BE GOOD ...
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Answer 1

Answer:

$\frac{15}{ \sqrt{10} + \sqrt{20} + \sqrt{40} + \sqrt{5} - \sqrt{80} }$

$= \frac{15}{ \sqrt{10} + \sqrt{4 \times 5} + \sqrt{4 \times 10} + \sqrt{5} - \sqrt{16 \times 5} }$

$= \frac{15}{ \sqrt{10} + 2 \sqrt{5} + 2\sqrt{10} + \sqrt{5} -4 \sqrt{5} }$

$= \frac{15}{3 \sqrt{10} + 3 \sqrt{5} - 4 \sqrt{5} }$

$= \frac{15}{ 3 \sqrt{10} - \sqrt{5} }$

Rationalise the denominator:

$= \frac{15}{(3 \sqrt{10} - \sqrt{5} ) } \times \frac{(3 \sqrt{10} + \sqrt{5}) }{(3 \sqrt{10} + \sqrt{5} )}$

$= \frac{15(3 \sqrt{10} + \sqrt{5} )}{ {(3 \sqrt{10} })^{2} - ({ \sqrt{5}) }^{2} }$

$= \frac{15(3 \sqrt{10} + \sqrt{5} )}{90 - 5}$

$= \frac{15(3 \sqrt{10} + \sqrt{5} )}{85}$

$= \frac{3(3 \sqrt{10} + \sqrt{5} )}{17}$

or,

$= \frac{3 \sqrt{5} (3 \sqrt{2} + 1) }{17}$