CBSE Class 9CBSE
Share
Notifications

View all notifications

Simplify (5 + Sqrt3)/(5 - Sqrt3) + (5 - Sqrt3)/(5 + Sqrt3) - CBSE Class 9 - Mathematics

Login
Create free account


      Forgot password?

Question

Simplify:

`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`

Solution

We know that rationalization factor for `sqrt5 - sqrt3` and `sqrt5 + sqrt3` are `sqrt5 + sqrt3` and `sqrt5 - sqrt3`  respectively.

We will multiply numerator and denominator of the given expression  `(sqrt5 + sqrt3)/(sqrt5 - sqrt3)` and `(sqrt5 - sqrt3)/(sqrt5 + sqrt3)` by `sqrt5 + sqrt3` and `sqrt5 + sqrt3` respectively, to get

`(sqrt5 + sqrt3)/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) + (sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) = ((sqrt5)^2 + (sqrt3)^2 +  2 xx sqrt5 xx sqrt3)/((sqrt5)^2- (sqrt3)^2)`

`(5 + 3 + 2sqrt15)/(5- 3) + (5 + 3 - 2sqrt15)/(5 - 3)`

`= (5 + 3 + 2sqrt15 + 5 + 3 - 2sqrt15)/2`

= 16/2

= 8

Hence the given expression is simplified to 8

 

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Solution Simplify (5 + Sqrt3)/(5 - Sqrt3) + (5 - Sqrt3)/(5 + Sqrt3) Concept: Operations on Real Numbers.
S
View in app×