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# Simplify 2/(Sqrt5 + Sqrt3) + 1/(Sqrt3 + Sqrt2) + 3/(Sqrt5 + Sqrt2) - CBSE Class 9 - Mathematics

ConceptOperations on Real Numbers

#### Question

Simplify

2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) + 3/(sqrt5 + sqrt2)

#### Solution

We know that rationalization factor for sqrt5 + sqrt3, sqrt3 + sqrt2 and sqrt5 + sqrt2 are sqrt5 - sqrt3, sqrt3 - sqrt2 and sqrt5 - sqrt2 respectively. We will multiply numerator and denominator of the given expression 2/(sqrt5 + sqrt3), 1/(sqrt3 + sqrt2) and 3/(sqrt5 + sqrt2) by 2 - sqrt3, sqrt5 + sqrt3 and 2 + sqrt5respectively to get

2/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) + 1/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) - 3/(sqrt5 + sqrt2) xx (sqrt5  - sqrt2)/(sqrt5 - sqrt2) = (2sqrt5 - 2sqrt3)/(5 - 3) + (sqrt3 - sqrt2)/(3 - 2) - (3sqrt5 - 3sqrt2)/(5 - 2)

 = (2sqrt5 - 2sqrt3)/2 + (sqrt3 - sqrt2)/1 - (3sqrt5 - 3sqrt2)/3

= sqrt5 - sqrt3 + sqrt3 - sqrt2 - sqrt5 + sqrt2

= 0

Hence the given expression is simplified to 0

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Solution Simplify 2/(Sqrt5 + Sqrt3) + 1/(Sqrt3 + Sqrt2) + 3/(Sqrt5 + Sqrt2) Concept: Operations on Real Numbers.
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