103 LearnersLast updated on May 26th, 2025
Square Root of 4500
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 4500.
What is the Square Root of 4500?
The square root is the inverse of the square of the number. 4500 is not a perfect square. The square root of 4500 is expressed in both radical and exponential form. In the radical form, it is expressed as √4500, whereas (4500)^(1/2) in the exponential form. √4500 ≈ 67.082, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers, and q ≠ 0.
Finding the Square Root of 4500
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used. Instead, 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 4500 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4500 is broken down into its prime factors:
Step 1: Finding the prime factors of 4500
Breaking it down, we get 2 × 2 × 3 × 3 × 5 × 5 × 5: 2² × 3² × 5³
Step 2: Now we found out the prime factors of 4500. The second step is to make pairs of those prime factors. Since 4500 is not a perfect square, the digits of the number can’t be grouped completely into pairs. Therefore, calculating 4500 using prime factorization is impossible to find an exact square root.
Square Root of 4500 by Long Division Method
The long division method is particularly used for 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 4500, we need to group it as 00 and 45.
Step 2: Now we need to find n whose square is less than or equal to 45. We can say n as ‘6’ because 6 × 6 = 36 is less than 45. Now the quotient is 6, and after subtracting 36 from 45, the remainder is 9.
Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 6 + 6, and we get 12, which will be our new divisor.
Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n ≤ 900. Let us consider n as 7, 127 × 7 = 889.
Step 5: Subtract 889 from 900, the difference is 11, and the quotient is now 67.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1100.
Step 7: Now we need to find the new divisor, which is 134 because 1348 × 8 = 10784.
Step 8: Subtracting 10784 from 11000, we get the result 216.
Step 9: Now the quotient is 67.08.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √4500 is approximately 67.08.
Square Root of 4500 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 4500 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4500. The smallest perfect square less than 4500 is 4225, and the largest perfect square greater than 4500 is 4624. √4500 falls somewhere between 65 and 68.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Using the formula (4500 - 4225) ÷ (4624 - 4225) = 275 ÷ 399 ≈ 0.6882 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 65 + 0.6882 ≈ 65.6882, so the square root of 4500 is approximately 67.08 when further refined.
Common Mistakes and How to Avoid Them in the Square Root of 4500
Students do make mistakes while finding the square root, like 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: √50 ≈ 7.07, there is also -7.07 which should not be forgotten.
Square Root of 4500 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4500?
The area of the square is approximately 4500 square units.
Explanation
The area of the square = side².
The side length is given as √4500.
Area of the square = side² = √4500 × √4500 = 4500.
Therefore, the area of the square box is approximately 4500 square units.
Problem 2
A square-shaped building measuring 4500 square feet is built; if each of the sides is √4500, what will be the square feet of half of the building?
2250 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4500 by 2 = we get 2250.
So half of the building measures 2250 square feet.
Problem 3
Calculate √4500 × 5.
335.41
Explanation
The first step is to find the square root of 4500, which is approximately 67.08.
The second step is to multiply 67.08 with 5.
So 67.08 × 5 ≈ 335.41.
Problem 4
What will be the square root of (4500 - 450)?
The square root is approximately 65.57.
Explanation
To find the square root, we need to find the difference of (4500 - 450). 4500 - 450 = 4050, and then √4050 ≈ 65.57.
Therefore, the square root of (4500 - 450) is approximately ±65.57.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4500 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle is approximately 234.16 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4500 + 50) = 2 × (67.08 + 50) = 2 × 117.08 ≈ 234.16 units.
FAQ on Square Root of 4500
1.What is √4500 in its simplest form?
2.Mention the factors of 4500.
3.Calculate the square of 4500.
4.Is 4500 a prime number?
5.4500 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 4500?
8.How do technology and digital tools in India support learning Algebra and Square Root of 4500?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 4500
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 25 is a perfect square because it is 5².
- Prime factorization: Breaking down a number into its prime factors. Example: The prime factorization of 4500 is 2 × 2 × 3 × 3 × 5 × 5 × 5.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number step-by-step to get an approximate value.
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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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