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Simplify the Following Expressions: (Sqrt5 - 2)(Sqrt3 - Sqrt5) - Mathematics

Simplify the following expressions:

`(sqrt5 - 2)(sqrt3 - sqrt5)`

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Solution

 We can simplify the expression `(sqrt5 - 2)(sqrt3 - sqrt5)` as

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

`= sqrt15 - sqrt(5 xx 5) - 2sqrt3 + 2sqrt5`

`=sqrt15 - (5^2)^(1/2) - 2sqrt3 +2sqrt5`

`= sqrt15 - (5^2)^(1/2) - 2sqrt3 + 2sqrt5`

`= sqrt15 - 5^1 - 2sqrt3 + 2sqrt5`

Hence the value of the expression is `sqrt15 - 2sqrt3 + 2sqrt5 - 5`

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.1 | Q 2.3 | Page 2
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