Question

What is a decomposition reaction?

Answer 1

Answer:

11-6√3 = a -b√3

where a=11 and b =6

Step-by-step explanation:

Step(i):-

Given

      $\frac{5+2\sqrt{3} }{7+4\sqrt{3} }$

Rationalize

=    $\frac{5+2\sqrt{3} }{7+4\sqrt{3} } X \frac{7-4\sqrt{3} }{7-4\sqrt{3} }$

=    $\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{7^{2} -(4\sqrt{3})^{2} }$

=  $\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{49-16(3) }$

= $\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{1 }$

Step(ii):-

Multiply

    ${(5+2\sqrt{3})(7-4\sqrt{3} ) }$

=  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