Name: Patterns of Square Numbers
Uploaded: 2019-07-19
Duration: 9 min 26 s
Description: Did you know that square numbers form various patterns? The square of any odd natural number apart from 1 can be expressed as the sum of two consecutive natu...

Question

Find the square root by the long division method: $19321$

Accepted Answer

Given, $19321$

Steps of long division method for finding square roots:

Step $1 .$ Group the digits in pairs, starting with the digit in the units place. Each pair and the remaining digit (if any) is called a period.

Step $2 .$ Think of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.

Step $3 .$ Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.

Step $4 .$ Now, the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend.

Step $5 .$ Repeat steps $2, 3$ and $5$ till all the periods have been taken up. Now, the quotient so obtained is the required square root of the given number.

$\begin{matrix} 1 & 3 & 9 \\ 1 & 1 & \bar{93} & \bar{21} \\ - & 1 \\ 2 & 3 & 93 \\ - & 69 \\ 26 & 9 & 24 & 21 \\ - & 24 & 21 \\ 0 \end{matrix}$

Hence, $\sqrt{19321} = 139$

Find the square root by the long division method: $19321$

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root by the long division method: 19321

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root by the long division method: $19321$