124 LearnersLast updated on May 26th, 2025
Square Root of 1454
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 various fields such as architecture, physics, and finance. Here, we will discuss the square root of 1454.
What is the Square Root of 1454?
The square root is the inverse of the square of the number. 1454 is not a perfect square. The square root of 1454 is expressed in both radical and exponential form. In the radical form, it is expressed as √1454, whereas (1454)^(1/2) in exponential form. √1454 ≈ 38.111, 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 1454
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 1454 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1454 is broken down into its prime factors:
Step 1: Finding the prime factors of 1454 Breaking it down, we get 2 x 727: 2^1 x 727^1
Step 2: Now we found out the prime factors of 1454. The second step is to make pairs of those prime factors. Since 1454 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1454 using prime factorization is not feasible for finding its square root.
Square Root of 1454 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 1454, we need to group it as 54 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 x 3 = 9, which is less than 14. Now the quotient is 3, after subtracting 9 from 14 the remainder is 5.
Step 3: Now let us bring down 54, which is the new dividend. Add the old divisor with the same number 3 + 3, and we get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the previous quotient times two. Now we have 6n as the new divisor, and we need to find the value of n such that 6n x n ≤ 554.
Step 5: Let n be 8; 68 x 8 = 544
Step 6: Subtract 544 from 554, the difference is 10, and the quotient is 38.
Step 7: 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 1000.
Step 8: Now we need to find the new divisor, which is 761 because 7611 x 1 = 761.
Step 9: Subtracting 761 from 1000, we get the result 239.
Step 10: Now the quotient is 38.1
Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √1454 is approximately 38.11.
Square Root of 1454 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 1454 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √1454.
The smallest perfect square less than 1454 is 1444, and the largest perfect square more than 1454 is 1521. √1454 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1454 - 1444) / (1521 - 1444) = 10 / 77 ≈ 0.13
Using the formula, we identified the decimal approximation of our square root. The next step is adding the value we got initially to the decimal number: 38 + 0.13 = 38.13, so the square root of 1454 is approximately 38.13.
Common Mistakes and How to Avoid Them in the Square Root of 1454
Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of these mistakes 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 usually take only the positive square root, as it is the one commonly required.
For example, √50 = 7.07; 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 children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the next step.
For example, √(12 + 24) = √12 + √24 is the wrong application of 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 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 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 root and square root consistently 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. This may happen while subtracting or elsewhere in the process.
Square Root of 1454 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1454?
The area of the square is approximately 1454 square units.
Explanation
The area of the square = side^2.
The side length is given as √1454.
Area of the square = side^2 = √1454 x √1454 = 1454.
Therefore, the area of the square box is approximately 1454 square units.
Problem 2
A square-shaped garden measuring 1454 square feet is planted; if each of the sides is √1454, what will be the square feet of half of the garden?
727 square feet
Explanation
We can just divide the given area by 2 since the garden is square-shaped.
Dividing 1454 by 2, we get 727.
So, half of the garden measures 727 square feet.
Problem 3
Calculate √1454 x 5.
Approximately 190.55
Explanation
The first step is to find the square root of 1454, which is approximately 38.11.
The second step is to multiply 38.11 by 5.
So, 38.11 x 5 = 190.55.
Problem 4
What will be the square root of (1444 + 10)?
The square root is approximately 38.13.
Explanation
To find the square root, first, find the sum of (1444 + 10). 1444 + 10 = 1454, and then √1454 ≈ 38.13.
Therefore, the square root of (1444 + 10) is approximately 38.13.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1454 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is approximately 156.22 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1454 + 40) = 2 × (38.11 + 40) = 2 × 78.11 = 156.22 units.
FAQ on Square Root of 1454
1.What is √1454 in its simplest form?
2.Mention the factors of 1454.
3.Calculate the square of 1454.
4.Is 1454 a prime number?
5.1454 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 1454?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1454?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1454
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse of squaring is finding the square root, so √16 = 4.
- Irrational number: An irrational number cannot be written as a simple fraction; it cannot be expressed as a ratio of two integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is typically used in real-world applications, thus known as the principal square root.
- Prime factorization: Breaking down a number into its basic prime number factors.
- Long division method: A method used to divide numbers and find square roots, especially for non-perfect squares.
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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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