Question

How do you simplify 1 over square root 2?

Answer 1

Hint: In the given question, we have been asked what is the value of 1 divided by the square root of 2. First, we are going to represent the number in mathematical form. Then, we are going to shift the irrational part in the denominator to the numerator by rationalizing it. Then we just solve the fraction as normal.

Complete step-by-step answer:
1 over square root 2 is written as \[\dfrac{1}{{\sqrt 2 }}\].
First, we rationalize the denominator.
\[\dfrac{1}{{\sqrt 2 }} \times \dfrac{{\sqrt 2 }}{{\sqrt 2 }} = \dfrac{{\sqrt 2 }}{2}\]
Now, \[\sqrt 2 = 1.414\]
So, \[\dfrac{{\sqrt 2 }}{2} = \dfrac{{1.414}}{2} = 0.707\]

Note: When the denominator is an irrational number, we have to shift the irrational part to the numerator by rationalizing the denominator. Then we just solve and simplify.