Question

What is a
decomposition reaction?

Answer 1

11-6√3 = a -b√3

where a=11 and b =6

Explanation:

Step(i):-

Given

`(5+2√(3) )/(7+4√(3) )`

Rationalize

=
`(5+2√(3) )/(7+4√(3) ) X (7-4√(3) )/(7-4√(3) )`

=
`((5+2√(3))(7-4√(3) ) )/(7^(2) -(4√(3))^(2) )`

=
`((5+2√(3))(7-4√(3) ) )/(49-16(3) )`

=
`((5+2√(3))(7-4√(3) ) )/(1 )`

Step(ii):-

Multiply

`{(5+2√(3))(7-4√(3) ) }`

= 5 × 7 - 5×4√3 + 2√3 ×7 - 2√3 × 4√3

= 35 -20√3+ 14√3-8×3

= 35 - 6√3 -24

= 11-6√3