Question

Is the expression $\sqrt{24\times 25}$ a surd?

• A. yes
• B. no

Answer 1

The correct option is A yes

Simplify $\sqrt{24\times 25}$

$\Rightarrow \sqrt{24\times 25}=\sqrt{2\times 2\times 2\times 3\times 5\times 5}=\sqrt{2^2}\times \sqrt{2\times 3}\times \sqrt{5^2}=2\times \sqrt{6}\times 5=10\sqrt{6}$

So, $\sqrt{24\times 25}$ is $10$ multiplied by $\sqrt{6}$ where $\sqrt{6}$ is an irrational number. Multiplication of a rational number $10$ with an irrational number $\sqrt{6}$ will give an irrational number.
Hence, $10\sqrt{6}$ is a surd.