129 LearnersLast updated on May 26th, 2025
Square Root of 5450
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 5450.
What is the Square Root of 5450?
The square root is the inverse of the square of a number. 5450 is not a perfect square. The square root of 5450 is expressed in both radical and exponential form. In the radical form, it is expressed as √5450, whereas (5450)^(1/2) in the exponential form. √5450 ≈ 73.793, 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 5450
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 5450 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5450 is broken down into its prime factors:
Step 1: Finding the prime factors of 5450 Breaking it down, we get 2 x 5 x 5 x 109: 2^1 x 5^2 x 109^1
Step 2: Now that we have found the prime factors of 5450, the second step is to make pairs of those prime factors. Since 5450 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating √5450 using prime factorization directly is not possible.
Square Root of 5450 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 5450, we need to group it as 50 and 54.
Step 2: Now we need to find n whose square is 54. We can say n is ‘7’ because 7 x 7 = 49, which is lesser than or equal to 54. Now the quotient is 7, after subtracting 54 - 49, the remainder is 5.
Step 3: Now let us bring down 50, forming the new dividend of 550. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.
Step 4: The new divisor will have a tenths digit to form 14n. We need to find a digit for n so that 14n x n is less than or equal to 550. Let us consider n as 3, now 143 x 3 = 429.
Step 5: Subtract 429 from 550, the difference is 121, and the quotient is 73.
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 12100.
Step 7: Now we need to find the new divisor, which is 147, because 1473 x 3 = 4419.
Step 8: Subtracting 4419 from 12100, we get the result 7681.
Step 9: Continue doing these steps until you get two numbers after the decimal point. If there is no decimal value, continue till the remainder is zero.
So the square root of √5450 ≈ 73.793
Square Root of 5450 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 5450 using the approximation method.
Step 1: Now we have to find the closest perfect square of √5450.
The smallest perfect square less than 5450 is 5184 and the largest perfect square greater than 5450 is 5625. √5450 falls somewhere between 72 and 75.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula: (5450 - 5184) ÷ (5625 - 5184) ≈ 0.793
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 72 + 0.793 ≈ 72.793, so the square root of 5450 is approximately 72.793.
Common Mistakes and How to Avoid Them in the Square Root of 5450
Students make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 consider only the positive square root, as it is the required one in most contexts.
For example, √50 ≈ 7.071, but there is also -7.071, 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 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 steps.
For example: √(12 + 24) = √12 + √24 is the wrong method of using roots. The right way 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 students is to simplify the numbers inside the square root. This helps in identifying the approximate value accurately.
For example: √50 = 7 is incorrect; 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 roots and square roots constantly, 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 at the end. This may happen during subtraction or elsewhere.
Square Root of 5450 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5450?
The area of the square is approximately 5450 square units.
Explanation
The area of the square = side^2.
The side length is given as √5450.
Area of the square = side^2 = √5450 x √5450 = 5450.
Therefore, the area of the square box is approximately 5450 square units.
Problem 2
A square-shaped building measuring 5450 square feet is built; if each of the sides is √5450, what will be the square feet of half of the building?
2725 square feet
Explanation
We can just divide the given area by 2 since the building is square-shaped.
Dividing 5450 by 2 = we get 2725
So half of the building measures 2725 square feet.
Problem 3
Calculate √5450 x 5.
368.965
Explanation
The first step is to find the square root of 5450, which is approximately 73.793.
The second step is to multiply 73.793 with 5.
So, 73.793 x 5 ≈ 368.965
Problem 4
What will be the square root of (5450 + 4)?
The square root is approximately 74.
Explanation
To find the square root, we need to find the sum of (5450 + 4). 5450 + 4 = 5454, and then √5454 ≈ 74.
Therefore, the square root of (5450 + 4) is approximately ±74.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5450 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 297.586 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√5450 + 50) = 2 × (73.793 + 50) = 2 × 123.793 = 297.586 units.
FAQ on Square Root of 5450
1.What is √5450 in its simplest form?
2.Mention the factors of 5450.
3.Calculate the square of 5450.
4.Is 5450 a prime number?
5.5450 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 5450?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 5450?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 5450
- 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.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, the positive square root, known as the principal square root, is often used due to its relevance in real-world applications.
- Prime factorization: A process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of non-perfect squares by dividing and averaging.
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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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