Question

Find the square root of the following decimal numbers by division method:
$5.774409$.

Answer 1

Hint: Here, we are required to find the square root of the given decimal number. Hence, we will use the division method and then, solve it further to find the required square root of the given decimal number which when multiplied by itself will give the original number.

Complete step-by-step answer:
According to the question, in order to find the square root of $5.774409$ using Division method,
We will follow the following steps:

\[ 2\begin{array}{*{20}{l}}
   | {2.403} \\
\hline
   | {\overline 5 .\overline {77} \overline {44} \overline {09} } \\
   | { - 4}
\end{array} \\
  44\left| \!{\overline {\,
  177 \\
   - 176 \\ \,}} \right. \\
  480\left| \!{\overline {\,
  144 \\
   - 0 \\ \,}} \right. \\
  4803\left| \!{\overline {\,
  14409 \\
  \underline { - 14409} \\
  0 \\ \,}} \right. \\ \]

In this method, we start pairing the numbers by taking a bar starting from the unit’s place. We take the largest possible number whose square will be less than or equal to the leftmost pair.
Now, we double the value of the quotient and assume it as a ten’s place digit and for the one’s place we have to take a digit such that multiplying the total number by that digit, we get a number less than or equal to the carried down number. Since, the remainder is 0 in this question; hence, the given number is a perfect square.

Therefore, the square root of $5.774409$ is $2.403$
Hence, this is the required answer.

Note:
In mathematics, a decimal number can be defined as a number whose whole number part and the fractional part are separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one. In order to find a square root of any number we should know that the square root of any number means the value which when multiplied by itself, gives the original number. Thus, we use the division method to find the square root of decimal numbers.