Question

What is the square root of $3$ divided by $3$ $?$

Answer 1

Hint: To solve the question we need to know the concept of square root. We should know that a number could be written as the product of the square root of the same number. It means $a$ could be written as the product of $\sqrt{a}$, which could be mathematically represented as $a=\sqrt{a}\times \sqrt{a}$ . The fraction could be brought to simple form if the numerator and denominator has a common factor except$1$.

Complete step by step solution:
The question asks us to divide the square root of $3$ by $3$. We are aware of the fact that $3$ is a prime number which means $3$ has only two factors which are $1$ and $3$. Thus it means that the square root of $3$ will never give us a natural number.
The question asks to divide the number $\sqrt{3}$ with $3$. On doing so we get:
$\Rightarrow {\displaystyle \frac{\sqrt{3}}{3}}$
On seeing the fraction we can confirm that there is a common number $3$ is in both numerator and denominator of the fraction. So we can write $3$ as the product of $\sqrt{3}$, on writing it mathematically we get:
$\Rightarrow 3=\sqrt{3}\times \sqrt{3}$
On substituting $3$ with the above value we get:
$\Rightarrow {\displaystyle \frac{\sqrt{3}}{\sqrt{3}\times \sqrt{3}}}$
Since $\sqrt{3}$, is common in both numerator and denominator it will get cancelled. Hence giving the value to be
$\Rightarrow \left({\displaystyle \frac{\sqrt{3}}{\sqrt{3}}}\right)\left({\displaystyle \frac{1}{\sqrt{3}}}\right)$
The above fraction will result in:
$\Rightarrow {\displaystyle \frac{1}{\sqrt{3}}}$
On changing the number in decimal form we get
$\Rightarrow {\displaystyle \frac{1}{1.732}}$
$\Rightarrow 0.577$

$\therefore$ The square root $3$ divided by $3$ is ${\displaystyle \frac{1}{\sqrt{3}}}$which in decimal form is $0.577$.

Note: The square root of the prime number is never a natural number. The back calculation can justify whether the answer is correct or not. For checking the answer we will have to consider the function, where $a$ is an unknown value,
${\displaystyle \frac{\sqrt{a}}{3}}={\displaystyle \frac{1}{\sqrt{3}}}$
On cross-multiplying and calculating the value for $a$ we get:
$\Rightarrow {\displaystyle \frac{1}{\sqrt{3}}}\times 3$
$\Rightarrow {\displaystyle \frac{3}{\sqrt{3}}}$
On further calculation we get the value of $a$ as
$\Rightarrow \sqrt{a}=\sqrt{3}$
$\Rightarrow a=3$
So the value of $a$ hence found matches with the question, showing the answer to be right.