124 LearnersLast updated on May 26th, 2025
Square Root of 1024
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.
What is 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.
Finding the Square Root of 1024
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.
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1024 by Prime Factorization Method
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.
Square Root of 1024 by Long Division Method
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.
Square Root of 1024 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1024
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically take only the positive square root, as it is the required one in most practical scenarios.
For example, √1024 = 32, but there is also -32 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before proceeding.
For example: √(16 + 36) = √52 is correct, not √16 + √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be constantly taught the difference between cube root and square root, as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, resulting in a wrong answer. This may happen during subtraction or elsewhere.
Square root of 1024 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √1024 x 5.
160
Explanation
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.
Problem 4
What will be the square root of (1000 + 24)?
The square root is 32.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1024 + 38)
= 2 × (32 + 38)
= 2 × 70
= 140 units.
FAQ on Square Root of 1024
1.What is √1024 in its simplest form?
2.Mention the factors of 1024.
3.Calculate the square of 1024.
4.Is 1024 a prime number?
5.1024 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1024?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1024?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1024
- Square root: A square root is the inverse of a square. Example: 4^2 =16 and the inverse of the square is the square root that is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 1024 is a perfect square because it is 32^2.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, 1024 is 2^10.
- Perimeter: Perimeter is the total distance around the edge of a figure. For example, the perimeter of a rectangle is calculated as 2 × (length + width).
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Jaskaran Singh Saluja
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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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