Question

Find the square root of 3136 by division method.
(a) 56
(b) 66
(c) 46
(d) 36

Answer 1

Hint: To find the square root of 3136, write the number in pairs. Follow the procedure for calculating the square root of the given number. The quotient after performing long division of the number is the square root of the given number.

Complete step-by-step answer:
We have to calculate the square root of 3136 by division method.
To do so, we will begin by grouping the digits in pairs starting the pairing from units place. $$\overline{31}\overline{36}$$
We will now take the largest number as a divisor whose square is less than or equal to the number in the first pair. We will divide the dividend by the divisor and write the quotient and remainder.
$5\stackrel{5}{\stackrel{―}{)\begin{array}{rl}& \stackrel{―}{31}\stackrel{―}{36}\\ & \underset{―}{25}\\ & 6\end{array}}}$
We will now bring down the next pair of numbers to the right side of the remainder.
$5\stackrel{5}{\stackrel{―}{)\begin{array}{rl}& \stackrel{―}{31}\stackrel{―}{36}\\ & \underset{―}{25}\\ & 636\end{array}}}$
We will double the quotient and enter it with a blank of the right side. We will select the largest number which can be placed at the unit place of the divisor, which when multiplied by the new digit at units place, gives a number less than or equal to dividend.
We will divide the dividend by the divisor and write quotient and remainder. We will repeat the process until the remainder is zero.
$106\stackrel{56}{\overline{)\begin{array}{rl}& \stackrel{―}{31}\stackrel{―}{36}\\ & \underset{―}{25}\\ & 636\\ & \underset{―}{636}\\ & \underset{―}{000}\end{array}}}$
The quotient is the square root of the given number. Thus, we have $\sqrt{3136}=56$.
Hence, the square root of 3136 is 56, which is option (a).

Note: We must pair up the numbers before calculating the square root of the number. Also, one must keep in mind that pairing should be done from units place. Otherwise, we will get an incorrect answer.