Question

Simplify root 4/3+root 7 by rationalizing the denominator​

Answer 1

6 - 2
`√(7)`

Explanation:

using the rule of radicals

•
`√(a)` ×
`√(a)` = a

given

`(4)/(3+√(7) )`

to rationalise the denominator , multiply the numerator and denominator by the conjugate of the denominator

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

=
`(4(3-√(7)) )/((3+√(7))(3-√(7)) )` ← expand denominator using FOIL

=
`(12-4√(7) )/(9-3√(7)+3√(7)-7 )`

=
`(12-4√(7) )/(2)`

=
`(12)/(2)` -
`(4√(7) )/(2)`

= 6 - 2
`√(7)`