Question

Write the following surd $\sqrt{2}$ in exponential form?

Answer 1

Hint: To write any form in exponential form means we have to write the given expression into a number with some exponent. As you can see that in the given problem, we have been given a square root expression so converting this surd into the exponential form we have to remove the square root sign and will write 2 with some exponent.

Complete step by step answer:
In the above problem, we have given the surd $\sqrt{2}$ and we are asked to write this surd in the exponential form. And we know that the exponential form of any number is the number with some exponent.
Now, we are going to convert the surd $\sqrt{2}$ into exponential form. As we know that $\sqrt{2}$ is the square root of 2 so to write the exponential form of this surd we are going to write 2 with the exponent of $\dfrac{1}{2}$. The mathematical form of what we have just described is written below:
${{2}^{\dfrac{1}{2}}}$
From the above solution, we have written the exponential form of the given surd $\sqrt{2}$ as ${{2}^{\dfrac{1}{2}}}$.

Note: In the above problem, we have written the square root in the exponential form. Similarly, if we have given cube root, fourth root or ${{n}^{th}}$ root of any number then we are going to write the exponential form of these numbers by writing number with the exponent of $\dfrac{1}{3}$ for cube root, for the fourth root we are going to write the number with the exponent of $\dfrac{1}{4}$ and for ${{n}^{th}}$ root, we are going to write the number with the exponent of $\dfrac{1}{n}$. And the mathematical expression will look as follows:
Cube root of a number say (x):
${{x}^{\dfrac{1}{3}}}$
Fourth root of a number say (x):
${{x}^{\dfrac{1}{4}}}$
${{n}^{th}}$ root of a number say (x):
${{x}^{\dfrac{1}{n}}}$