Question

What is $\dfrac{3}{\sqrt{3}}?$

Answer 1

Hint: We know that for a number $a,$ the product of its square root value to itself, that is $\sqrt{a}\sqrt{a},$ gives the number itself. We can write this as $a=\sqrt{a}\sqrt{a}.$ If we transpose one of the root values to the left-hand side, we will get $\dfrac{a}{\sqrt{a}}=\sqrt{a}.$

Complete step by step solution:
Let us consider the given problem. We are asked to find what $\dfrac{3}{\sqrt{3}}$ is.
Before that, we should know what this expression means.
We know that the given number is a fraction. A fraction is a number which has a numerator and a denominator. When we write a number as a fraction, we mean to say that the numerator is divided by the denominator. We know that all the integers can be written as a fraction by setting $1$ as the denominator for any number divided by $1$ gives the same number.
So, in the given problem, we are asked to find the value when $3$ is divided by $\sqrt{3}.$
We know that the number $3$ can be written as a product of $\sqrt{3}$ and $\sqrt{3}.$ Because, we have the identity that says $a=\sqrt{a}\sqrt{a}.$ If we transpose one of the root values to the left-hand side, we will get $\dfrac{a}{\sqrt{a}}=\sqrt{a}.$
That is, ${{\left( \sqrt{3} \right)}^{2}}=3.$
Again, we can write this as $3=\sqrt{3}\sqrt{3}.$
Let us transpose one of the terms from the right-hand side to the left-hand side to get $\dfrac{3}{\sqrt{3}}=\sqrt{3}.$

Hence the value of $\dfrac{3}{\sqrt{3}}$ is $\sqrt{3}.$

Note: The identity $a=\sqrt{a}\sqrt{a}$ is true for any number $a.$ Here, we have dealt with the square and the square root of a number. When we divide the ${{n}^{th}}$ power of a number with the number, we will get the ${{\left( n-1 \right)}^{th}}$ power of the number, $\dfrac{{{a}^{n}}}{a}={{a}^{n-1}}.$