Evaluate using long division method: $\sqrt{7056}$

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Detailed Solution

The following is a division formula for calculating the square root of
(a) Starting with the unit digit, place a bar over every pair of digits. If the number of digits is odd, add a bar to the leftmost single digit as well.
(b) Consider the greatest number whose square is even with but lower than the initial digit of the bar. Take this integer both as the quotient and the divisor.
(c) Bring down the next pair of digits that have a bar to the right of the remainder, which becomes a new dividend, and then subtract the product of the divisor and the quotient from the first bar digit.
(d) The initial divisor and quotient are now added, and a digit must be added to the right side of that sum in accordance with the new dividend, which must be chosen so that the product of the new divisor and this digit is less than or equal to the new dividend.
(e) Repeat steps (b, c, d) till the bar digit has been taken up. Now quotient is the required square root of the given number.
Now, let us find out the square root of 7056. Now, putting the bars on digits from behind we can represent the number as

= 7056^{¯}

Now, by the first step try to think of a number whose square is just less than 70.

8^{2} < 70 < 9^{2}

So, put 8 in divisor and quotient both we get,

https://www.vedantu.com/question-sets/a041e721-ec2e-4c5c-a0e7-034860246b286889642213088644872.png

Now, add the quotient digit to the divisor we get,

https://www.vedantu.com/question-sets/0002ebca-7415-44d1-8369-e54df1426960167439175117783759.png

Now, we need to put the same number 16 (in divisor) and in the quotient such that multiplication of divisor formed after putting the digit and the same digit in the quotient as well. So we get