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We can find the square root of decimals by converting it into rational numbers. Examples
1) √1.44 = √144/√100 = 12/10 = 1.2
2) √0.0081 = √81/√10000 = 9/100 = 0.09
First convert 37.0881 into a rational number and then find the square root by prime factorization or long division method.
√37.0881 = √(370881/10000)
But √370881 = 609
√10000 = 100
∴ √37.0881 = 609 / 100
________________________________________________________________ Square Root of Decimal Number
We may find the square root of a decimal number without converting it into a rational number. We do it as follows :
Example : √21.16
Step 1: To find the square root of a decimal number we put bars on the integral part
(i.e., 21) of the number in the usual manner.And place bars on the decimal part (i.e., 16) on every pair of digits beginning with the first decimal place. Proceed as usual. We get
Step 2 :Now proceed in a similar manner. The left most bar is on 21 and 42 < 21 < 52.
Take this number as the divisor and the number under the left-most bar as the
dividend, i.e., 21. Divide and get the remainder.
Step 3 The remainder is 1. Write the number under the next bar (i.e., 16) to the right of
this remainder, to get 116.
Step 4 :Add the divisor 2 and quotient 2 that gives us 4.
Step 5 : Think of a largest number in fill in the blank in such a way that the product of a new divisor and this digit is equal to or less than 516(new dividend).
Since 16 is the decimal part so put a decimal point in the quotient.
In this case 86 × 6 = 516.
As 86× 6 = 516 so we choose the new digit as 6. Get the remainder.
Step 6: Since the remainder is 0 and no bar left, therefore √21.16 = 4.6