Question

What is $\sqrt{3}$?

Answer 1

Hint: We first use the division of square root process to find the square root of 3. We use the concept for both integer and decimal to find the value of $\sqrt{3}$ till the 3-digit place after decimal.

Complete step-by-step answer:
We first have to find and check if the number 3 is a square number or not. 3 is a prime number and that’s why it can’t be broken in factored form.
We take 2 digits as a set from the right end and complete the division. For decimal form we take the set from the right side of the decimal.
\[\begin{align}
  & 1 \\
 & 1\left| \!{\overline {\,
 \begin{align}
  & \overline{3}.\overline{00}\overline{00} \\
 & \underline{1} \\
 & 2.000 \\
\end{align} \,}} \right. \\
\end{align}\]
Now we have to enter the decimal part. We keep doing the breaking ion the set form till 3-digit place after decimal.
\[\begin{align}
  & 1.732 \\
 & 27\left| \!{\overline {\,
 \begin{align}
  & \overline{2}\overline{00}\overline{00}\overline{00} \\
 & \underline{189} \\
 & 1100 \\
\end{align} \,}} \right. \\
 & 343\left| \!{\overline {\,
 \begin{align}
  & 1100\overline{00} \\
 & \underline{1029} \\
 & 7100 \\
\end{align} \,}} \right. \\
 & 3462\left| \!{\overline {\,
 \begin{align}
  & 7100 \\
 & \underline{6924} \\
 & 176 \\
\end{align} \,}} \right. \\
\end{align}\]
Therefore, the value of $\sqrt{3}$ is $1.732$.
So, the correct answer is “$1.732$”.

Note: The long-division method and arranging the set of 2 digits is different for integer and decimal. But taking double for the next division and putting a particular number is the same process for both of them. Since 3 is a non-perfect square number, we will find the value of root 3 using the long division method as shown above.