Question

Write the simplest form of rationalising factor of the given surd: \[\sqrt {50} \]

Answer 1

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.

Complete step-by-step answer:
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.

Note:Make sure that the rationalizing factor that you find is in the simplest form if it is particularly mentioned in the question. The rationalizing factor that you find is perfectly correct only if it provides a rational number after multiplying the rationalizing factor with it. Be careful with the calculations. We can also observe that the product of two similar surds is always a rational number and they are rationalizing factors to each other though it may not be the simplest form.