Question

Find the \[\sqrt {39204} \].

Answer 1

Hint: Here we will use the long division method to find out the square root of the number. First, we will pair the digits of the numbers then we will divide it to get its square root. The square root of a number is the factor that we multiply by itself two times to get that number.

Complete step-by-step answer:
Given number is \[\sqrt {39204} \].
First, we will pair the digits of the number given. As the number is an odd digit number. Therefore the first digit is keep as a single and the other digits are paired, we get
\[\sqrt {\overline 3 \,\overline {92} \,\overline {04} } \]
Now we will divide the pairs with their maximum divisor. Therefore firstly we will divide the 3 with the maximum divisor, we get
           $1$
$1) \overline{\overline{1}\;\overline{92}\;\overline{04}} \\
\,\,\,\,\,\underline{1} $
    $292$
Now, with the remain of the first division the next pair of digits get in and now we will divide this number with the maximum divisor, we get

           $19$
$1) \overline{\overline{1}\;\overline{92}\;\overline{04}} \\
\,\,\,\,\,\underline{1} $
$29) \overline{292} \\
\,\,\,\,\,\,\,\,\underline{261} $
       $03104$

Now, again with the remain of the second division the next pair of digits get in and now we will divide this number with the perfect divisor, we get

           $198$
$1) \overline{\overline{1}\;\overline{92}\;\overline{04}} \\
\,\,\,\,\,\underline{1} $
$29) \overline{292} \\
\,\,\,\,\,\,\,\,\underline{261} $
 $388)\overline{03104} \\
\,\,\,\,\,\,\,\,\,\,\,\underline{3104}$
             $0$

So, we can see that the square root of the given number is equal to 198.
Hence the value of \[\sqrt {39204} \] is equal to 198.

Note: Here we have to remember that always in these types of questions we have to simplify the equation and make the equation free from any kind of roots. Unlike square root the cube root of a number is the factor that we multiply by itself three times to get that number. So, we should not get confused between square root and cube root.
Square root is expressed as \[\sqrt[2]{{{\rm{number}}}}\]
Cube root is expressed as \[\sqrt[3]{{{\rm{number}}}}\]