Question

Please help. Free the denominator of the fractionfrom irrationality:


`(2)/(5 √(3) )`

`( √(5 ) + 2 )/( √(5) - 2)`
​

Answer 1

see explanation

Explanation:

Given

`(2)/(5√(3) )`

To rationalise the denominator, multiply the numerator/ denominator by
`√(3)`

=
`(2√(3) )/(5√(3)(√(3)) )`

=
`(2√(3) )/(15)`

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Given

`(√(5)+2 )/(√(5)-2 )`

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of
`√(5)` - 2 is
`√(5)` + 2 , then

=
`((√(5)+2)(√(5)+2) )/((√(5)-2)(√(5)+2) )` ← expand numerator/denominator using FOIL

=
`(5+4√(5)+4 )/(5-4)`

=
`(9+4√(5) )/(1)`

= 9 + 4
`√(5)`