# 5 + sqr root 3 divide by 5 - sqr root 3 rationalise the denominator in each expression

justaguide | Certified Educator

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We have to rationalize the denominator in (5 + sqrt 3)/ ( 5 - sqrt 3)

This can be done by multiplying the numerator and denominator by ( 5 + sqrt 3). Using the relation (a - b)(a + b) = a^2 - b^2 gives a rational denominator

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

=> (5 + sqrt 3)^2 / ( 5^2 - (sqrt 3)^2)

=> (25 + 3 + 10 sqrt 3) / ( 25 - 3)

=> (28 + 10 sqrt 3) / 22

=> (14 + 5* sqrt 3) / 11

The required result is: (14 + 5* sqrt 3) / 11

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academicsfirst | Certified Educator

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The question asks us to rationalize the denominator in the expression 5 + sqrt 3 divided by 5 - sqrt 3.

=> Multiply the numerator and denominator by the conjugate:

[(5 + sqrt 3)/(5 - sqrt 3)] * [ (5 + sqrt 3)/5 + sqrt 3)

=> ( 25 + 10 sqrt 3 + 3)/(25 - 3)

=> (28 + 10 sqrt 3)/(22)

Simplify the fraction:

=> (14 + 5 sqrt3)/(11)

The answer is (14 + 5 sqrt3)/(11).

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