Question

Find the product of following with its conjugate pair.

$4\sqrt{3}+\sqrt{27}$

• A. conjugate pair $=4\sqrt{3}+\sqrt{27}$, product $12$
• B. conjugate pair $=4\sqrt{3}+\sqrt{27}$, product $21$
• C. conjugate pair $=4\sqrt{3}-\sqrt{27}$, product $21$
• D. conjugate pair $=4\sqrt{3}-\sqrt{27}$, product $20$

Answer 1

The correct option is C conjugate pair $=4\sqrt{3}-\sqrt{27}$, product $21$

The conjugate pair is
$4\sqrt{3}-\sqrt{27}$
And the product is
$(4\sqrt{3}+\sqrt{27})(4\sqrt{3}-\sqrt{27})$
$={\left(4\sqrt{3}\right)}^2-{\left(\sqrt{27}\right)}^2$
$=16\times 3-27$
$=48-27=21$