142 LearnersLast updated on May 26th, 2025
Square Root of 4356
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 4356.
What is the Square Root of 4356?
The square root is the inverse of the square of the number. 4356 is a perfect square. The square root of 4356 is expressed in both radical and exponential form. In the radical form, it is expressed as √4356, whereas (4356)^(1/2) in the exponential form. √4356 = 66, 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 4356
The prime factorization method can be used for perfect square numbers. For non-perfect square numbers, methods like the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4356 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4356 is broken down into its prime factors.
Step 1: Finding the prime factors of 4356
Breaking it down, we get 2 x 2 x 3 x 3 x 11 x 11: 2^2 x 3^2 x 11^2
Step 2: Now we found out the prime factors of 4356. The second step is to make pairs of those prime factors. Since 4356 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √4356 using prime factorization is possible.
Square Root of 4356 by Long Division Method
The long division method is particularly used for both perfect and 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 4356, we need to group it as 56 and 43.
Step 2: Now we need to find n whose square is ≤ 43. We can say n is ‘6’ because 6 x 6 = 36, which is less than 43. Now the quotient is 6, and after subtracting 36 from 43, the remainder is 7.
Step 3: Now let us bring down 56, which is the new dividend. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 12n x n ≤ 756. Let us consider n as 6, now 12 x 6 x 6 = 756.
Step 6: Subtract 756 from 756, the difference is 0, and the quotient is 66.
Step 7: Since the remainder is zero, we have completely determined the square root.
So the square root of √4356 is 66.
Square Root of 4356 by Approximation Method
The approximation method is another method for finding 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 4356 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4356. The closest perfect square to 4356 is itself, as 66 x 66 = 4356. Using this method, we conclude that the square root of 4356 is exactly 66.
Common Mistakes and How to Avoid Them in the Square Root of 4356
Students do make mistakes while finding the square root, such as 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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √4356 = 66, there is also -66 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root 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 and then move on to the second step. For Example: √(36 + 64) = √36 + √64 is wrong. The right way is √(36 + 64) = √100 = 10.
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 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from 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, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 4356 Examples
Problem 1
Can you help Max find the perimeter of a square box if its side length is given as √4356?
The perimeter of the square is 264 units.
Explanation
The perimeter of the square = 4 × side.
The side length is given as √4356.
Perimeter of the square = 4 × √4356 = 4 × 66 = 264.
Therefore, the perimeter of the square box is 264 units.
Problem 2
A square-shaped tile measuring 4356 square feet is created; if each of the sides is √4356, what will be the square feet of half of the tile?
2178 square feet
Explanation
We can just divide the given area by 2 as the tile is square-shaped.
Dividing 4356 by 2 = we get 2178.
So half of the tile measures 2178 square feet.
Problem 3
Calculate √4356 x 5.
330
Explanation
The first step is to find the square root of 4356, which is 66, the second step is to multiply 66 with 5.
So 66 x 5 = 330.
Problem 4
What will be the square root of (4356 + 144)?
The square root is 70.
Explanation
To find the square root, we need to find the sum of (4356 + 144). 4356 + 144 = 4500, and then √4500 ≈ 67.08.
Therefore, the approximate square root of (4356 + 144) is ±67.08.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4356 units and the width ‘w’ is 44 units.
The perimeter of the rectangle is 220 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4356 + 44) = 2 × (66 + 44) = 2 × 110 = 220 units.
FAQ on Square Root of 4356
1.What is √4356 in its simplest form?
2.Mention the factors of 4356.
3.Calculate the square of 4356.
4.Is 4356 a prime number?
5.4356 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 4356?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 4356?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 4356
- Square root: A square root is the inverse of a square. Example: 8^2 = 64 and the inverse of the square is the square root, that is, √64 = 8.
- Perfect square: A number that has an integer as its square root. Example: 64 is a perfect square because √64 = 8.
- Rational number: A rational number is a number that can be expressed as the quotient of two integers, p/q, where q is not equal to zero.
- Long division method: A method used to calculate the square root of a number using a step-by-step division process.
- Prime factorization: Expressing a number as the product of its prime numbers. For example, the prime factorization of 4356 is 2^2 x 3^2 x 11^2.
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About BrightChamps in United Arab Emirates
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
