126 LearnersLast updated on May 26th, 2025
Square Root of 1450
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 1450.
What is the Square Root of 1450?
The square root is the inverse of the square of the number. 1450 is not a perfect square. The square root of 1450 is expressed in both radical and exponential form. In the radical form, it is expressed as √1450, whereas in the exponential form it is (1450)^(1/2). √1450 ≈ 38.07887, 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 1450
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 1450 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1450 is broken down into its prime factors.
Step 1: Finding the prime factors of 1450 Breaking it down, we get 2 x 5 x 5 x 29: 2^1 x 5^2 x 29^1
Step 2: Now we found out the prime factors of 1450. The second step is to make pairs of those prime factors. Since 1450 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 1450 using prime factorization is not straightforward.
Square Root of 1450 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 1450, we need to group it as 50 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, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 50, which makes the new dividend 550. Add the old divisor with the same number, 3 + 3, we get 6 which will be part of our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 550. Let us consider n as 8; now 68 x 8 = 544.
Step 5: Subtract 544 from 550; the difference is 6, and the quotient is 38.
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 600.
Step 7: Now we need to find the new divisor, which is 761 because 761 x 1 = 761 is larger than 600. Try with 760 x 0.
Step 8: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √1450 ≈ 38.078.
Square Root of 1450 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 1450 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1450.
The smallest perfect square less than 1450 is 1444 (38^2), and the largest perfect square greater than 1450 is 1521 (39^2). √1450 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) Going by the formula (1450 - 1444) / (1521 - 1444) = 6/77 ≈ 0.078
Using the formula, we identified the decimal point for our square root. The next step is adding the value we got initially to the decimal number, which is 38 + 0.078 ≈ 38.078, so the square root of 1450 is approximately 38.078.
Common Mistakes and How to Avoid Them in the Square Root of 1450
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. 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 typically consider only the positive square root, as it is the required one in most practical applications.
For example, for √1450 ≈ 38.078, there is also -38.078 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root 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 proceeding to the next step.
For example, √(12 + 24) = √36 is correct, whereas √12 + √24 is incorrect.
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 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, which results in a wrong answer at the end. This may happen in subtraction or elsewhere in the process.
Square root of 1450 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1450?
The area of the square is approximately 1450 square units.
Explanation
The area of the square = side^2.
The side length is given as √1450.
The area of the square = side^2 = √1450 x √1450 = 1450.
Therefore, the area of the square box is approximately 1450 square units.
Problem 2
A square-shaped building measuring 1450 square feet is built; if each of the sides is √1450, what will be the square feet of half of the building?
725 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1450 by 2 = we get 725.
So half of the building measures 725 square feet.
Problem 3
Calculate √1450 x 5.
Approximately 190.39
Explanation
The first step is to find the square root of 1450, which is approximately 38.078.
The second step is to multiply 38.078 by 5.
So 38.078 x 5 ≈ 190.39.
Problem 4
What will be the square root of (1450 + 50)?
The square root is approximately 40.
Explanation
To find the square root, we need to find the sum of (1450 + 50). 1450 + 50 = 1500, and then √1500 ≈ 38.73.
Therefore, the square root of (1450 + 50) is approximately ±38.73.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1450 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 176.16 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1450 + 50) = 2 × (38.078 + 50) = 2 × 88.078 ≈ 176.16 units.
FAQ on Square Root of 1450
1.What is √1450 in its simplest form?
2.Mention the factors of 1450.
3.Calculate the square of 1450.
4.Is 1450 a prime number?
5.1450 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 1450?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1450?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 1450
- 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, it is always the positive square root that has more prominence due to its uses in the real world. This is why it is also known as the principal square root.
- Prime factorization: The process of breaking down a number into its prime number components.
- Perfect square: A number that is the square of an integer.
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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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