Question

What is the reciprocal of the square root of 2?

Answer 1

Hint: For solving this question you should know about the calculation of the square root of any positive number. And also you should know to take the reciprocal of any number. The reciprocal of any number is equal to the 1-power of that number or we can say that it is inverse of that number.

Complete step by step solution:
According to the question we have to find the reciprocal of the square root of 2.
As we know that the square root of any digit is equal to the \[{1}/{2}\;\] power of that. Or we can say that if we take the root of this then it will be equal to the square root of that term or that digit.
And the reciprocal of any term is equal to the – 1 power of that term or inverse of that term.
We can calculate the square root of any terms if it is a positive term then it is very much easy and can be calculated directly but if it is negative then it is easy to find the square root of that but in this the values will be imaginary and this value does not exist. And if we calculate the square root of a positive number with decimal then it will also be very tough. Because it is solved by heron's formula.
So, according to our question we have to calculate the reciprocal of the square root of 2.
So, the square root of y \[\Rightarrow \sqrt{{{x}^{2}}}\]
 \[y\Rightarrow x\]
According to our question we can write it as,
\[{{x}^{2}}=2\]
So, the y is equal to:
 \[y=\sqrt{2}\]
Reciprocal of the square root of 2 is:
\[\begin{align}
 & \Rightarrow \dfrac{1}{y}=\dfrac{1}{\sqrt{2}} \\
&\Rightarrow\dfrac{1}{y}=\dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2} \\
\end{align}\]
So, the reciprocal of the square root of 2 is \[\dfrac{\sqrt{2}}{2}\].

Note: During the calculation of this question you should be careful for the square root. Because if the value will be negative then it will be solved from different methods and if positive then from the different method and if positive then from the different method. And take the reciprocal and make the denominator complete.