Question

# Write the simplest form of rationalising factor of the given surd: $\sqrt {50}$

Hint:After reading the question carefully, first try to know what is the rationalising factor, then by converting the given surd into the simplest form, you can identify the simplest form of the rationalising factor of the given surd. So, follow the below step by step process to get a relevant explanation.

$\sqrt {50}$ can be written in the simplest form,
$\Rightarrow \sqrt {25 \times 2} = 5\sqrt 2$
Because the square root of $25$ is $5$.
Now to find out the simplest form of rationalizing factor of given surd, multiply it with $\sqrt 2$.
$= 5\sqrt 2 \times \sqrt 2$
$= 5 \times 2$ (Since, $\sqrt 2 \times \sqrt 2 = 2$)
$= 10$
As $10$ is a rational number, $\sqrt 2$ is a rationalizing factor for the given surd and it is also the simplest form.