Question

Find the square root of the following number by division method: 28224

Answer 1

Division method for finding square roots.

Step 1: Fist place a bar over every pair of digits starting from the unit digit, if the no. of digits are add then the left most single digit will also have a bar.

Step 2: Think of the largest number whose square is equal to or just less than the first bar digit. take this number as the divisor and also as the quotient

Step 3: Next subtract the product of the divisor and the quotient from the first bar and digit and bring down the next pair of digit which have bar to the right side of the reminder. Thus becomes the new dividend.

Step 4: Now the new division is obtained by adding the first divisor and the quotient and a digit to the right side of it that we have to choose, according to the new dividend. which is chosen in such a way that product of new divisor and this digit is less than or equal to the new dividend.

Step 5: Repeat steps 2, 3 , 4 till the bar digits have been taken up. Now the quotient is the required square root of the given no.

To find the square root of $28224$

Step 1: $\overline{2}\overline{82}\overline{24}$

Step 2: $1^2<2<2^2$

$1<2<4$

Step 3: The new dividend is $182$

Step 4: $22\times 2=44$

$23\times 3=69$

$24\times 4=94$

$25\times 5=125$

$26\times 6=156<182$

$27\times 7=189>182$

The new divisor is 26.

Step 5: The next new dividend is $2624$ and new divisor is $328$

$322\times 2=644$

$323\times 3=969$

$324\times 4=1296$

$325\times 5=1625$

$328\times 8=2624$

The square root of $28224$ is $168$.