130 LearnersLast updated on May 26th, 2025
Square Root of 4624
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 4624.
What is the Square Root of 4624?
The square root is the inverse of the square of the number. 4624 is a perfect square. The square root of 4624 is expressed in both radical and exponential form. In the radical form, it is expressed as √4624, whereas (4624)^(1/2) in the exponential form. √4624 = 68, 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 4624
The prime factorization method is 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 4624 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4624 is broken down into its prime factors.
Step 1: Finding the prime factors of 4624
Breaking it down, we get 2 × 2 × 2 × 2 × 17 × 17: 2^4 × 17^2
Step 2: Now we found out the prime factors of 4624. The second step is to make pairs of those prime factors. Since 4624 is a perfect square, we can group the factors into pairs of 2^2 × 17. Therefore, the square root of 4624 using prime factorization is 2^2 × 17 = 68.
Square Root of 4624 by Long Division Method
The long division method is particularly used for perfect and non-perfect square numbers. In this method, we find the square root using a step-by-step division approach.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 4624, we group it as 46 and 24.
Step 2: Now we need to find a number whose square is less than or equal to 46. We can use 6 because 6 × 6 = 36, which is less than 46. Now the quotient is 6.
Step 3: Subtract 36 from 46; the remainder is 10. Bring down the next pair of digits, 24, making the new dividend 1024.
Step 4: Double the quotient and write it as the new divisor with a blank digit next to it (12_).
Step 5: Find a digit to fill the blank such that when you multiply the new divisor by this digit, the product is less than or equal to 1024. The digit is 8, making the divisor 128.
Step 6: 128 × 8 = 1024; subtracting gives a remainder of 0.
So the square root of √4624 is 68.
Square Root of 4624 by Approximation Method
The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 4624 using the approximation method.
Step 1: Find numbers whose squares are close to 4624. The perfect squares closest to 4624 are 4624 itself. Since 4624 is a perfect square, the approximation method directly confirms the square root as 68.
Common Mistakes and How to Avoid Them in the Square Root of 4624
Students make mistakes while finding square roots, sometimes forgetting about the negative square root or skipping steps in the long division method. 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 often take only the positive square root for practical purposes.
For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving to the next step.
For example: √(12+24) = √12 + √24 is incorrect.
The correct method is √(12 + 24) = √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 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots, 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, and students might skip a step accidentally, leading to a wrong answer. This may occur in subtraction or elsewhere in the process.
Square Root of 4624 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4624?
The area of the square is 4624 square units.
Explanation
The area of the square = side^2.
The side length is given as √4624.
Area of the square = side^2 = √4624 × √4624 = 68 × 68 = 4624.
Therefore, the area of the square box is 4624 square units.
Problem 2
A square-shaped building measuring 4624 square feet is built; if each of the sides is √4624, what will be the square feet of half of the building?
2312 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4624 by 2 gives us 2312.
So half of the building measures 2312 square feet.
Problem 3
Calculate √4624 × 3.
204
Explanation
The first step is to find the square root of 4624, which is 68.
The second step is to multiply 68 by 3.
So 68 × 3 = 204.
Problem 4
What will be the square root of (4000 + 624)?
The square root is 68.
Explanation
To find the square root, we need to find the sum of (4000 + 624). 4000 + 624 = 4624, and then √4624 = 68.
Therefore, the square root of (4000 + 624) is ±68.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4624 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 212 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4624 + 38) = 2 × (68 + 38) = 2 × 106 = 212 units.
FAQ on Square Root of 4624
1.What is √4624 in its simplest form?
2.Mention the factors of 4624.
3.Calculate the square of 68.
4.Is 4624 a prime number?
5.4624 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 4624?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 4624?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 4624
- 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 equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 4624 is a perfect square because it is 68^2.
- Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, 2^3 = 2 × 2 × 2 = 8.
- Divisor: A divisor is a number by which another number is divided. For example, in 4624 ÷ 68 = 68, 68 is the divisor.
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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.
