Last updated on May 26th, 2025
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the 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:
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.
Students do make mistakes while finding the square root, likewise forgetting about the negative square root. Skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √0.0009?
The area of the square is 0.00081 square units.
The area of the square = side².
The side length is given as √0.0009.
Area of the square = side² = √0.0009 × √0.0009
= 0.03 × 0.03
= 0.00081.
Therefore, the area of the square box is 0.00081 square units.
A square-shaped building measuring 0.001 square feet is built; if each of the sides is √0.001, what will be the square feet of half of the building?
0.0005 square meters
We can just divide the given area by 2 as the building is square-shaped.
Dividing 0.001 by 2 = we get 0.0005.
So half of the building measures 0.0005 square meters.
Calculate √0.001 × 5.
0.1581
The first step is to find the square root of 0.001 which is approximately 0.0316, the second step is to multiply 0.0316 with 5.
So 0.0316 × 5 = 0.1581.
What will be the square root of (0.0009 + 0.0001)?
The square root is 0.0316.
To find the square root, we need to find the sum of (0.0009 + 0.0001). 0.0009 + 0.0001 = 0.001, and then √0.001 = 0.0316.
Therefore, the square root of (0.0009 + 0.0001) is approximately ±0.0316.
Find the perimeter of the rectangle if its length ‘l’ is √0.0009 units and the width ‘w’ is 0.0001 units.
We find the perimeter of the rectangle as 0.0608 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.0009 + 0.0001)
= 2 × (0.03 + 0.0001)
= 2 × 0.0301
= 0.0602 units.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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