Square Root of 1001

The square root is the inverse of the square of the number. 1001 is not a perfect square. The square root of 1001 is expressed in both radical and exponential form. In the radical form, it is expressed as √1001, whereas (1001)^(1/2) in the exponential form. √1001 ≈ 31.6386, 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 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: -

1. Prime factorization method 
2. Long division method 
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 1001 is broken down into its prime factors.

Step 1: Finding the prime factors of 1001 Breaking it down, we get 7 x 11 x 13: 7¹ x 11¹ x 13¹

Step 2: Now we found out the prime factors of 1001. The second step is to make pairs of those prime factors. Since 1001 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 1001 using prime factorization yields an approximate square root value.

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 1001, we group it as 01 and 10.

Step 2: Now we need to find a number whose square is less than or equal to 10. We can say this number is 3 because 3 x 3 = 9, which is less than 10. Now the quotient is 3, after subtracting 9 from 10, the remainder is 1.

Step 3: Now bring down 01 which is the new dividend, making it 101. Add the old divisor with the same number (3 + 3) to get 6, which will be our new divisor.

Step 4: Find a digit 'd' such that 6d x d is less than or equal to 101. The value of 'd' is 1 because 61 x 1 = 61, which is less than 101.

Step 5: Subtract 61 from 101 to get 40. Since the remainder is 40, and the divisor is 61, we proceed with decimal places.

Step 6: Add a decimal point, allowing us to bring down two zeros, making the new dividend 4000.

Step 7: Now find a new digit 'd' such that (61d + d) x d is less than or equal to 4000. Continue this until reaching the desired precision.

So the square root of √1001 ≈ 31.6386.

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Let us learn how to approximate the square root of 1001.

Step 1: Find the closest perfect squares around 1001. The closest perfect square less than 1001 is 961, and the closest perfect square greater than 1001 is 1024. √1001 falls between 31 and 32.

Step 2: Apply the formula to approximate: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square)

Using the formula: (1001 - 961) / (1024 - 961) = 40 / 63 ≈ 0.6349 Step 3: Add this decimal to the lower perfect square root value: 31 + 0.6349 ≈ 31.6349

Therefore, the square root of 1001 is approximately 31.6349.

• Square root: A square root is the inverse of a square. For example, 5² = 25, and the inverse is the square root, i.e., √25 = 5.

• Irrational number: An irrational number cannot be expressed in the form of p/q, where q is not zero and p and q are integers.

• Principal square root: A number has both positive and negative square roots, but the positive square root is more commonly used. This is known as the principal square root.

• Prime factorization: The expression of a number as a product of its prime factors. For instance, 1001 = 7 x 11 x 13.

• Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square since it is 4².