Question

how to rationalize it?
$\frac{1}{2} \times \frac{ \sqrt{3} }{2( 1+ \sqrt{3}) }$




*Step by step*

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Answer 1

♠QUESTION♠

Rationalise:

»$\frac{1}{2} \times \frac{ \sqrt{3} }{2( 1+ \sqrt{3}) }$

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♦SOLUTION♦

ON SIMPLIFYING THE GIVEN EXPRESSION gives:

»$\frac{ \sqrt{3} }{4} \times \frac{1}{ \sqrt{3} + 1 }$

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NOW,

For Rationalising the denominator:

On multiplying both numerator and denominator by such an expression,

so as to convert numerator or denominator into an applicable identity.

E.g. Multiplying both numerator and denominator by "(√3–1)" gives:

»$\frac{ \sqrt{3} }{4} \times ( \frac{1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 } )$

»$\frac{ \sqrt{3} }{4} \times \frac{ \sqrt{3} - 1 }{( \sqrt{3}) {}^{2} - (1) {}^{2} }$

»$\frac{ \sqrt{3} }{4} \times \frac{ \sqrt{3} - 1}{3 - 1}$

»$\frac{ \sqrt{3} }{4} \times ( \frac{ \sqrt{3} - 1}{2} )$

»$\frac{( \sqrt{3} )( \sqrt{3} ) - (1)( \sqrt{3}) }{4 \times 2}$

»$\frac{3 - \sqrt{3} }{8}$

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♣ANSWER♣

»$\frac{1}{2} \times \frac{ \sqrt{3} }{2(1 + \sqrt{3}) } = \frac{3 - \sqrt{3} }{8}$

Answer 2

Your answer is in the attachment.

Hope it'll help.

~ A.R.M.Y ~