Question

Look at the rational expression shown below and rewrite it in simplified radical form. Please show ALL work!

(5-2√7)/(3-√7)

Thank you in advance!

Answer 1

`(1-√(7) )/(2)`

Explanation:

given
`(5-2√(7) )/(3-√(7) )`

To rationalise the denominator multiply the numerator/ denominator by the conjugate of the denominator.

the conjugate of 3 -
`√(7)` is 3 +
`√(7)`, hence

`(5-2√(7) )/(3-√(7) )` ×
`(3+√(7) )/(3+√(7) )`

= (15 + 5
`√(7)` - 6
`√(7)` - 14 ) / (9 - 7)

=
`(1-√(7) )/(2)` ← in simplified radical form