Question

Is the expression $\sqrt{12\times 27}$ a surd?

• A. yes
• B. no

Answer 1

The correct option is B no

Simplify $\sqrt{12\times 27}$

$\Rightarrow \sqrt{12\times 27}=\sqrt{(2\times 2\times 3)\times (3\times 3\times 3)}=\sqrt{(2\times 2)\times (3\times 3)\times (3\times 3)}=\sqrt{2^2}\times \sqrt{3^2}\times \sqrt{3^2}=2\times 3\times 3=18$
After the simplification, the simplified expression is $18$ which is a rational number.
So, $\sqrt{12\times 27}$ is not a surd.