Square Root of Decimals

We can find the square root of decimals by converting it into rational numbers.

1) √1.44 = √144/√100 = 12/10 = 1.2

2) √0.0081 = √81/√10000 = 9/100 = 0.09

3) √37.0881

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
= 6.09
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

Squares and Square roots

Introduction of Squares and Square Roots
Perfect Squares or not
Properties of Square Numbers
Short cut method to find squares
Introduction of Square Roots
Properties of Square Roots
Square root by Prime factorization method
Square root by long division method
Square root of rational numbers
Square root of Decimals
Square root by estimation method

From squares and square roots to Exponents

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