Square Root of 0.001

The square root is the inverse of the square of the number. 0.001 is not a perfect square. The square root of 0.001 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.001, whereas (0.001)^(1/2) in the exponential form. √0.001 = 0.031622776, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is generally used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
 

• Long division method
• Approximation method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 0.001, we need to group it as 00 and 01.

Step 2: Now we need to find n whose square is 0. We can say n as ‘0’ because 0 × 0 is lesser than or equal to 0. Now the quotient is 0 after subtracting 0-0 the remainder is 0.

Step 3: Now let us bring down 01 which is the new dividend. Add the old divisor with the same number 0 + 0 we get 0 which will be our new divisor.

Step 4: The new divisor will be 0n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 0n × n ≤ 1, let us consider n as 3, now 0.3 × 3 = 0.9.

Step 6: Subtracting 1 from 0.9, the difference is 0.1, and the quotient is 0.03.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 100.

Step 8: Now we need to find the new divisor that is 63 because 63 × 3 = 189.

Step 9: Subtracting 189 from 1000, we get the result 811.

Step 10: Now the quotient is 0.031.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue until the remainder is zero.

So the square root of √0.001 is approximately 0.0316.

The approximation method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 0.001 using the approximation method.

Step 1: Now we have to find the closest perfect square of √0.001. The smallest perfect square below 0.001 is 0.0001 and the largest perfect square above 0.001 is 0.01. √0.001 falls somewhere between 0.01 and 0.1.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (0.001 - 0.0001) ÷ (0.01 - 0.0001) = 0.0909. Using the formula we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 0.01 + 0.0909 = 0.031.

So the square root of 0.001 is approximately 0.031.

• Square root: A square root is the inverse of a square. Example: 0.1² = 0.01, and the inverse of the square is the square root, that is √0.01 = 0.1.
   
• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 0.001, 0.01, and 0.1 are decimals.
   
• Long division method: A manual calculation method used to find the square root of non-perfect squares through iterative steps.
   
• Approximation method: A method to estimate the square root of a number using nearby perfect squares to find a close decimal approximation.