LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SQUARE ROOT OF NON-PERFECT SQUARE NATURAL NUMBER

__To Find The Square Root of a NonPerfect Square Natural Number –__

**Step.1) Put a suitable number
of pairs of zeros after the decimal point, for example, 15 = 15.0000……..**

**Step.2) Now we have to find out the square root of the
number up to one more decimal place than the desired one.**

**Step.3) Now we have to round off the quotient**

**There are some example are given below for your better
understanding –**

**Example.1) Find out
the square root of 15**

**Answer) suppose
given number 15 is to be arranged like 15.000000**

**Step.1) First to find
out square root off 15, we would like to place a decimal point after 15 and then
put three pairs of zeros ‘0’ ( zero after decimal place have no value or not
define any value ) after decimal point. Now we would like to make the pairs of
digits of obtained number 15.000000, the pairs of digits, these are 15, 00, 00, & 00.**

**Step.2) The greatest
number the square of which does not exceeds 15 is 3. Write 3 in the quotient
place.**

**Step.3) Write 3² = 9
below 15 and subtract, obtained reminder is 6.**

**Step.4) So, now we
will put the first pair digit 00 just after obtained reminder 6. So the new
dividend is 600.**

**Step.5) So, now
multiply 2 with quotient 3 and we obtained the product 6 which will be
considered as the divisor and this is to be placed or put in divisor position. **

**Step.6)**** The largest possible digit that can be written next
to 6 such that the product of the new number and that digit does not exceed 600 is 8, write 8 next to 3 in the quotient place.**

**Step.7) Write 8 X 68 = 544 below the dividend and subtract.
Now we have a reminder, which is 56.**

**Step.8) So, now we will put second pair digit 00 just after
obtained reminder 56. So the new dividend is 5600.**

**Step.9) So, now multiply 2 with quotient 38 and the obtained
product 76 which will be considered as divisor and to be placed or put in
divisor position. **

**Step.10) The largest possible digit that can be written next
to 76 such that the product of the new number and that digit does not exceed 5600 is 7, write 7 next to 38 in the quotient’s place.**

**Step.11) Write 7 X 767 = 5369 below the dividend and
subtract. We find the reminder 231**

**Step.12) So, now we will put second pair digit 00 just after
obtained reminder 231. So the new dividend is 23100.**

**Step.13) So, now multiply 2 with quotient 387 and the
obtained product 774 which will be considered as divisor and to be placed or
put in divisor position. **

**Step.14) The largest possible digit that can be written next
to 774 such that the product of the new number and that digit does not exceed 23100 is 2, write 2 next to 387 in the quotient’s place.**

**Step.15) Write 2 X 7742 = 15484 below the dividend and
subtract. We find the reminder 7616, and the process continues…… as per the
zero you have entered after decimal places.**

**Step.16) The decimal point is placed in the quotient when
the first pair of the digits of the decimal part is written in the dividend. **

**Now, after placement
decimal point the obtained quotient would be 3.872 and correct to two decimal
places the required number would be = 3.87**

** So, √15 = √3.87² =
3.87 (Ans.)**

**Example.2) Find out
the square root of 19**

**Answer) Suppose given number 19 is to be arranged
like 19.000000**

**Step.1) First to find
out square root off 19, we would like to place a decimal point after 19 and then
put three pairs of zeros ‘0’ ( zero after decimal place have no value or not
define any value ) after decimal point. Now we would like to make the pairs of
digits of obtained number 19.000000, the pairs of digits, these are 19, 00, 00, & 00.**

**Step.2) The greatest
number the square of which does not exceeds 19 is 4. Write 4 in the quotient
place.**

**Step.3) Write 4² = 16
below 19 and subtract, obtained reminder is 3.**

**Step.4) So, now we
will put the first pair digit 00 just after obtained reminder 3. So the new
dividend is 300.**

**Step.5) So, now
multiply 2 with quotient 4 and we obtained the product 8 which will be
considered as the divisor and this is to be placed or put in divisor position. **

**Step.6)**** The largest possible digit that can be written next
to 8 such that the product of the new number and that digit does not exceed 300
is 3, write 3 next to 4 in the quotient place.**

**Step.7) Write 3 X 83 = 249 below the dividend and subtract.
Now we have a reminder, which is 51.**

**Step.8) So, now we will put second pair digit 00 just after
obtained reminder 51. So the new dividend is 5100.**

**Step.9) So, now multiply 2 with quotient 43 and the obtained
product 86 which will be considered as divisor and to be placed or put in
divisor position. **

**Step.10) The largest possible digit that can be written next
to 86 such that the product of the new number and that digit does not exceed 5100 is 5, write 5 next to 43 in the quotient’s place.**

**Step.11) Write 5 X 865 = 4325 below the dividend and subtract.
We find the reminder 775.**

**Step.12) So, now we will put second pair digit 00 just after
obtained reminder 775. So the new dividend is 77500.**

**Step.13) So, now multiply 2 with quotient 435 and the
obtained product 870 which will be considered as divisor and to be placed or
put in divisor position. **

**Step.14) The largest possible digit that can be written next
to 870 such that the product of the new number and that digit does not exceeds
77500 is 8, write 8 next to 435 in the quotient’s place.**

**Step.15) Write 8 X 8708 = 69664 below the dividend and
subtract. We find the reminder 7836, and the process continues…… as per the
zero you have entered after decimal places.**

**Step.16) The decimal point is placed in the quotient when
the first pair of the digits of the decimal part is written in the dividend. **

**Now, after placement decimal point the obtained quotient
would be 4.358 and correct to two decimal places the required number would be =
4.36**

** So, √19 = √4.36² =
4.36 (Ans.)**