Question

What is the square root of $\dfrac{1}{2}$ ?

Answer 1

Hint: To find the square root of $\dfrac{1}{2}$ , initially we will write the number in square root form and if the number is not a perfect square we will use a rationalization method i.e., multiply and divide the number using denominator and then solve to get the final answer.

Complete step by step answer:
The square root of $\sqrt {\dfrac{1}{2}}=? $
Further solving this square root part,
$\sqrt {\dfrac{1}{2}} = \dfrac{{\sqrt 1 }}{{\sqrt 2 }}$
Here, $\sqrt 1 = 1$ as $1$ is a perfect square of $1$.
So, the number becomes $\dfrac{1}{{\sqrt 2 }}$.
The number $2$ is not a perfect of any number, so we will rationalize it by multiplying and dividing the denominator number by the denominator itself, we get,
$\dfrac{1}{{\sqrt 2 }} \times \dfrac{{\sqrt 2 }}{{\sqrt 2 }}$
Solving this we get,
$\dfrac{{1 \times \sqrt 2 }}{{\sqrt 2 \times \sqrt 2 }}$

If we multiply any number with $1$ , we get the number itself.
Therefore, $1 \times \sqrt 2 $ is $\sqrt 2 $ and $\sqrt 2 \times \sqrt 2 = 2$ .
$\dfrac{{\sqrt 2 }}{2}$
But we can write $2$ as $\sqrt 2 \times \sqrt 2 $
$\dfrac{{\sqrt 2 }}{{\sqrt 2 \times \sqrt 2 }}$
One $\sqrt 2 $ from numerator and one $\sqrt 2 $ from denominator gets cancelled so we are left with,
$\dfrac{1}{{\sqrt 2 }}$
The value of $\sqrt 2 $ is $1.414$ .
$\therefore \dfrac{1}{{\sqrt 2 }} = \dfrac{1}{{1.414}} = 0.7071$

Therefore, the square root of $1/2$ is \[0.707\] .

Note: Square root of any number can be found out by two methods . First is square root by prime factorization and second is square root by long division. For square root by prime factorization, the number under the square root is factorized and is followed by pairing them in two numbers. Finding square roots for the imperfect numbers is a bit difficult but we can calculate using a long division method.