# Find the Value of 6/(Sqrt5 - Sqrt3) It Being Given that Sqrt3 = 1.732 And Sqrt5 = 2.236 - Mathematics

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Find the value of 6/(sqrt5 - sqrt3) it being given that sqrt3 = 1.732 and  sqrt5 = 2.236

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#### Solution

We know that rationalization factor for sqrt5 - sqrt3 is sqrt5 + sqrt3. We will multiply denominator and numerator of the given expression 6/(sqrt5 - sqrt3) by sqrt5 + sqrt3 to get

6/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) = (6sqrt5 + 6sqrt3)/((sqrt5)^2 - (sqrt3)^3)

= (6sqrt5 + 6sqrt3)/(5 - 3)

= (6sqrt5 + 6sqrt3)/2

= 3sqrt5 + 3sqrt3

Putting the values of sqrt5  and sqrt3 we get

3sqrt5 + 3sqrt3 = 3(2.236) + 3(1.732)

= 6.708 + 5.196

= 11.904

Hence value of the given expression is 11.904

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 7 | Page 15

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