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 the field of vehicle design, finance, etc. Here, we will discuss 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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √4624 × 3.
204
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.
What will be the square root of (4000 + 624)?
The square root is 68.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4624 + 38) = 2 × (68 + 38) = 2 × 106 = 212 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.