LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING ROOTS BY DIVISION METHOD

**FINDING ROOTS BY DIVISION METHOD**

**By Division Method –**

**1) First we have to make pairs of the digits of the given
number from to left, if the number of the digit is odd, alone digit will
remain at the extreme left of the
number, put a small line over each pair of digits.**

**2) Consider the first pair of digit (or the single unpaired
digit) from the left. This is the dividend, find the greatest number the square of
which is not more than the dividend. Write this number in the places of the
divisor and the quotient.**

**3) write the square of the number obtained in step 2 below
the dividend and subtract, find the reminder if any.**

**4) write the remainder obtained in step 3 along with the next
pair of digits of the given number, this new number is the new dividend.**

**5) write the first quotient just below the divisor and add
them.**

**6) write the largest possible digit on the right of the sum
(obtained in step 5) so the product of the new number and the largest possible
digit do not exceeds the new dividend. Subtract it from the new dividend.
This largest possible digit will be the second digit of the square root of the
given numbers.**

**7) Write the remainder obtained in step 6 along with the next
pair of digits of the given number. This number is the new dividend. Repeat the
process till all the pairs of the given number are exhausted.**

**Example –**

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**1) Find the square root of 13225**

**Step.1 – Here we can see that in the given number 13225,
extreme left number is odd pairs, so extreme left digit 1 will be alone and we
make pair with rest of the numbers such as 32 & 25**

**Step.2 – The greatest number, the square of which does not
exceeds 1, that is 1 itself, so we will write 1 in the divisors and quotient
places.**

**Step.3- Write 1², which is 1 and place below 1 and subtract.
The reminder is 0**

**Step.4- The new dividend is 32- the reminder along with the second pair.**

**Step.5- Write the quotient 1 below the divisor 1 and add or
multiply by 2 with quotient 1 **

**Step.6 – The largest possible digit that can be written next
to new obtained 2 such that the product of the new number and that digit does
not exceed 32 is 1 write the 1 next to
divisor and find 21 as the new divisor and place 1 in the quotient places.**

**Step.7 - Now we will
recall the table of 21 and we find 21 is the highest number which can be put below
32 and find the reminder 11.**

**Step.8 – Now we take the next pair of numbers which is 25 and
this number is placed after reminder 11, now the number stands 1125 which is
considered as a dividend.**

**Step.9 – Write the quotient 11 below the divisor 11 and
add or multiply by 2 with quotient 11 and we find 22.**

**Step.10 – The largest possible digit that can be written
next to new obtained 22 such that the product of the new number and that digit
does not exceeds 1125 is 5, so write the
5 next to divisor and find 225 as new
divisor and place 5 in the quotient places after 11.**

**Step.11****- Now we will
recall the table of 225 and we find 1125 is the highest number which can be put
below 1125 and find the remainder 0 .**

**Step.12 – So, we have got the final number as quotient which
is 115.**

**2) Find the square root of 1444**

**Step.1 – Here we can see that in the given number 1444,
extreme left number is even pairs, so we make a pair of the given numbers such as
14 & 44**

**Step.2 – The greatest number, the square of which does not
exceed 14, that is 3 itself, so we will write 3 in the divisors and quotient
places.**

**Step.3****- Write 3², which is 9 and place below 14 and
subtract. The remainder is 5**

**Step.4- The new dividend is 544 - the remainder along with the second pair.**

**Step.5- Write the quotient 3 below the divisor 3 and add or
multiply by 2 with quotient 3 **

**Step.6 – The largest possible digit that can be written next
to new obtained 6 such that the product of the new number and that digit does
not exceed 544 is 8 write the 8 next to
divisor and find 68 as new divisor and place 8 in the quotient places.**

**Step.7****- Now we will
recall the table of 68 and we find 544 is the highest number which can be put below
544 and find the remainder 0.**

**Step.8 – So, the desired obtained number as quotient is 38**