Question

Find the Square root of 21025 in long division method plz answer

Answer 1

Finding square root of a number by long division method:

Answer: $\sqrt{21025}$ = 145

Answer 2

Answer is 145

Step-by-step explanation:

Long Division Method:

• Set up a division with the number 21025 and by grouping every 2 digits of the dividend 21025 from right to left, we can rewrite as  2'10'25.  Starting from 1st group from left most, which is 2,  guess which square is maximum and less than or equal to 2.
• Because $1^2$ is less than 2, we can choose 1  as the quotient, and divisor. Place 1 on the right side and left side. Place  $1^2=1$ below 2. Now, (2-1 = 1) on subtracting 1 from 2, we get the remainder as 1.

• Bring down next group 10, place it after 1. Now the new dividend will become 110.  Place double of the quotient which is $1\times 2=2$ on the left side as the new divisor and reserve a room right side of it and the quotient.        

• Now guess a new quotient which is suitable to fill in both the blanks, such that the product of the new quotient and new divisor should be maximum and less than or equal to 110.  Select  4 as the new quotient and place it in the blanks. Now place the product of the new divisor and new quotient is $24 \times 4 = 96$ below 110, subtract it from 110, the remainder will be 14.

• Bring down the next group 25, place it after 14, then the new dividend is 1425.  Now place double of the quotient means 28 on the left side as the new divisor and put a blank after it and the quotient 14.

• We can estimate the new quotient from the formula $20 \times old\ quotient \times estimate= present\ dividend$.

•                                                  $20 \times 14 \times$ estimate = 1425
•                                                       estimate = $\frac {1425}{280}$ = 5.089

So we can choose 5 as a new quotient, such that the product of 285 and 5 is maximum and less than or equal to 1425.  Put 5 in both the blanks and place the product $285 \times 5$ = 1425 below 1425 and subtract.  The remainder is "0".