A square root of a number a is a number y such that y2 = a.
A number y whose square (the result of multiplying the number by itself, or (y × y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.
Another example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 × 3 = 9 and 3 is non-negative.
Square Root of Decimal Numbers
Steps to find Square root of decimal Numbers :-
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).
img src: ask-math
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
How to Find Square Root of Decimal Number without calculator
watch the detailed video given below carefully on how to find square root of decimal number in Hindi if you want to understand it clearly. This video will help you to better understand square root topic.