Question

Find the square root of the following number: 6084

Answer 1

Hint: To find the square root of 6084, first make the pairs of two numbers from left to right side of the given number, then divide by taking the value which is the perfect square.

Complete step-by-step answer:
Take the number and make the pair of the digits of given number from left side to right side,
$\underline {60} \underline {84} $
Start dividing the number 6084 so the first two terms of the number is 60; hence we have to take the value which has its square less than 60.
Taking 7 as divisor because the square of 7 is 49 which is less than 60 so we get,
$\begin{array}{*{20}{c}}
7\\
{\underline { + 7} }\\
{14}
\end{array}\mathop {\left| \!{\overline {\,
 \begin{array}{l}
6084\\
\underline {49 \downarrow \downarrow } \\
1184
\end{array} \,}} \right. }\limits^7 $
Now we have to take the value after 14 which should be multiply with itself then it will give 484 , so taking 8 which multiply with itself then give the required value hence we get,
\[\begin{array}{*{20}{c}}
7\\
{\underline { + 7} }\\
{148}\\
{\underline { + 8} }\\
{156}
\end{array}\mathop {\left| \!{\overline {\,
 \begin{array}{l}
6084\\
\underline {49 \downarrow \downarrow } \\
1184\\
\underline {1184} \\
0000
\end{array} \,}} \right. }\limits^{78} \]

Hence it is carried out that the square root of the 6084 is 78.

Note: Always keep in mind that you have to take the given values in pairs. If the given values have a total number of digits as an odd number, then take the first digit single and remaining values in pairs. After taking the values in pairs divide the value by the number which has its square less than the given number. You can also check your answer by multiplying the answer with itself. If the multiple is equal to the given value then the answer is correct otherwise check the mistake in the solution.