# CLASS-8FIND THE SQUARE ROOT OF DECIMAL NUMBER

To Find The Square Root of Decimal Number

Step.1) We have to make the pairs of the digit in the decimal part of the given number from left to right. Also, make pairs of the digits in an integral part of the given number from right to left. As usual, put a small line segment over each pair of the digit.

Step.2) Now we have to proceed to find the square root of the number, ignoring the decimal point.

Step.3) Place the decimal point in the quotient when you write the first pair of digits after the decimal point in the dividend.

For your better understanding, there are some example are given below -

1) Find the Square Root Of 60.84

Step.1)  Make the pairs of digits, these are 60 & 84.

Step.2)  First consider 1st pair, the greatest number the square of which does not exceeds 60 is 7. Write 7 in the quotient place.

Step.3)  Write 7²= 49 below 60 and subtract, obtained reminder is 11.

Step.4)  So, now we will put 2nd pair digit 84 just after obtained reminder 11. So the new dividend is 1184.

Step.5)  So, now multiply 2 with quotient 7 and we obtained the product 14 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 14 such that the product of the new number and that digit does not exceed 1184 is 8, write 8 next to 7 in the quotient place.

Step.7) Write 8 X 148 = 1184 below the dividend and subtract. Now we have no reminder after this, our work ends here.

Step.8) The decimal point is placed in the quotient when the first pair of the digits of the decimal part is written in the dividend.

So, √60.84 = √7.8² = 7.8      (Ans.)

2) Find The Square Root of 156.25

Step.1)  Make the pairs of digits, these are 56 & 25 but 1 is an unpaired digit

Step.2)  The greatest number the square of which does not exceeds 1 is 1. Write 1 in the quotient place.

Step.3) Write 1²= 1 below 1 and subtract, obtained reminder is 0.

Step.4) So, now we will put the first pair digit 56 just after obtained reminder 0. So the new dividend is 56.

Step.5) So, now multiply 2 with quotient 1 and we obtained the product 2 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 2 such that the product of the new number and that digit does not exceed 56 is 2, write 2 next to 1 in the quotient place.

Step.7) Write 2 X 22 = 44 below the dividend and subtract. Now we have a reminder, which is 12.

Step.8) So, now we will put second pair digit 25 just after obtained reminder 12. So the new dividend is 1225.

Step.9) So, now multiply 2 with quotient 12 and the obtained product 24 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 24 such that the product of the new number and that digit does not exceed 1225 is 5, write 5 next to 12 in the quotient place.

Step.11) Write 5 X 245 = 1225 below the dividend and subtract. As we have no reminder after this, our work ends here.

Step.12) The decimal point is placed in the quotient when the first pair of the digits of the decimal part is written in the dividend.

So, √156.25 = √12.5² = 12.5     (Ans.)