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Surd: A surd is an expression that consists of square root, cube root or other root symbol. Surds are used to write irrational numbers precisely.

Rationalising factor: The factor of multiplication by which rationalization is taken, that factor is called as rationalizing factor. If the product of two irrational numbers or surds is a rational number, then each surd is a rationalizing factor for each other.

\[\sqrt {50} \] 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.