Question

Find the square root of $5329$ by division method

Answer 1

Division method for finding square roots

step 1: First place a bar over every pair of digits starting from the unit digit, if the no. of digits is odd 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 a divisor and also as the quotient.

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

Step 4: The new divisor 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 all the bar digits have been taken up, new quotient is the required square root of the given no.

square root of the $\overline{53}\overline{29}$

Step 1: $5329$

Step 2: $49<53<64$ [Refer image 1]

$7^2<5^3<8^2$

Step 3: the new dividend is $429$ [Refer image 2]

Step 4: $142=\times 2=284$

$143\times 3=429$ [refer images 3]

This square root of $5329$ is $73$.