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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1024.
The square root is the inverse of squaring a number. 1024 is a perfect square. The square root of 1024 is expressed in both radical and exponential form. In the radical form, it is expressed as √1024, whereas 1024^(1/2) in the exponential form. √1024 = 32, which is a rational number because it can 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. Since 1024 is a perfect square, we can use the prime factorization method to find its square root.
The product of prime factors is the prime factorization of a number. Now let us look at how 1024 is broken down into its prime factors.
Step 1: Finding the prime factors of 1024 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2: 2^10
Step 2: Now we find the prime factors of 1024. The second step is to make pairs of those prime factors. As 1024 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, the square root of 1024 using prime factorization is 2^5 = 32.
The long division method is particularly useful for 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 1024, we need to group it as 10 and 24.
Step 2: Now we need to find a number n whose square is less than or equal to 10. We can say n is ‘3’ because 3 x 3 = 9 is less than 10. Now the quotient is 3, and after subtracting, 10 - 9, the remainder is 1.
Step 3: Now let us bring down 24, making the new dividend 124. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 124. Let's consider n as 2, now 62 x 2 = 124.
Step 5: Subtract 124 from 124; the remainder is 0.
Step 6: Since the remainder is zero, the quotient is 32.
So the square root of √1024 is 32.
Approximation method is another method for finding square roots, it is an easy method to find the square root of a given number. However, since 1024 is a perfect square, approximation is not necessary, but here's how it would work for non-perfect squares.
Step 1: Now we have to find the closest perfect square to √1024.
Since 1024 is a perfect square, √1024 = 32 is exact.
Students do make mistakes while finding the square root, including forgetting about negative square roots, 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 √1024?
The area of the square is 1024 square units.
The area of the square = side^2.
The side length is given as √1024.
Area of the square = side^2
= √1024 x √1024
= 32 x 32
= 1024.
Therefore, the area of the square box is 1024 square units.
A square-shaped building measuring 1024 square feet is built; if each of the sides is √1024, what will be the square feet of half of the building?
512 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1024 by 2 = 512.
So half of the building measures 512 square feet.
Calculate √1024 x 5.
160
The first step is to find the square root of 1024, which is 32.
The second step is to multiply 32 by 5.
So 32 x 5 = 160.
What will be the square root of (1000 + 24)?
The square root is 32.
To find the square root, we need to find the sum of (1000 + 24).
1000 + 24 = 1024, and then √1024 = 32.
Therefore, the square root of (1000 + 24) is ±32.
Find the perimeter of the rectangle if its length ‘l’ is √1024 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 140 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1024 + 38)
= 2 × (32 + 38)
= 2 × 70
= 140 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.
: He loves to play the quiz with kids through algebra to make kids love it.