125 LearnersLast updated on May 26th, 2025
Square Root of 1476
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 1476.
What is the Square Root of 1476?
The square root is the inverse of the square of the number. 1476 is not a perfect square. The square root of 1476 is expressed in both radical and exponential form. In the radical form, it is expressed as √1476, whereas (1476)^(1/2) in the exponential form. √1476 ≈ 38.4192, 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 1476
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1476 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1476 is broken down into its prime factors:
Step 1: Finding the prime factors of 1476 Breaking it down, we get 2 x 2 x 3 x 3 x 41: 2^2 x 3^2 x 41
Step 2: Now we have found the prime factors of 1476. The second step is to make pairs of those prime factors. Since 1476 is not a perfect square, grouping the digits into pairs is not possible.
Therefore, calculating 1476 using prime factorization directly is not feasible.
Square Root of 1476 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 1476, we need to group it as 76 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 76, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: Using the new divisor 6, find the largest single-digit n such that 6n x n is less than or equal to 576. Let n = 9: 69 x 9 = 621, which is too large. Try n = 8: 68 x 8 = 544.
Step 5: Subtract 544 from 576, the difference is 32, and the quotient is 38.
Step 6: Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3200.
Step 7: Find the new divisor by adding 8 to the previous divisor, giving 76. Determine n such that 760n x n is less than or equal to 3200. The appropriate n is 4, where 764 x 4 = 3056.
Step 8: Subtract 3056 from 3200, resulting in 144.
Step 9: The quotient is now 38.4. Continue this process until the desired decimal precision is reached.
So the square root of √1476 is approximately 38.42.
Square Root of 1476 by Approximation Method
The approximation method is another method for finding the 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 1476 using the approximation method.
Step 1: Identify the closest perfect squares of √1476.
The closest perfect squares are 1444 (38^2) and 1521 (39^2). √1476 falls between 38 and 39.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (1476 - 1444) ÷ (1521 - 1444) = 32 / 77 ≈ 0.416 Adding this decimal to the whole number we started with (38), we get approximately 38.416, so the square root of 1476 is approximately 38.42.
Common Mistakes and How to Avoid Them in the Square Root of 1476
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. 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 will be taking only the positive square root, as it is the required one.
For example: √50 = ±7.07, though we typically use the positive root.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that students make. We need to teach students that simplifying the numbers inside the square root is important before proceeding.
For example: √(12 + 24) ≠ √12 + √24. The correct method is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Simplifying the numbers inside the square root is important so students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7.071, not simply 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots to 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 in subtracting or elsewhere.
Square Root of 1476 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1476?
The area of the square is 1476 square units.
Explanation
The area of the square = side².
The side length is given as √1476.
Area of the square = side² = √1476 x √1476 = 1476.
Therefore, the area of the square box is 1476 square units.
Problem 2
A square-shaped garden measuring 1476 square feet is built; if each of the sides is √1476, what will be the square feet of half of the garden?
738 square feet
Explanation
We can just divide the given area by 2 since the garden is square-shaped.
Dividing 1476 by 2 = 738.
So half of the garden measures 738 square feet.
Problem 3
Calculate √1476 x 5.
192.096
Explanation
First, find the square root of 1476, which is approximately 38.42.
Then multiply 38.42 by 5.
So 38.42 x 5 = 192.096.
Problem 4
What will be the square root of (1476 + 44)?
The square root is 40.
Explanation
To find the square root, calculate the sum of (1476 + 44). 1476 + 44 = 1520, and then find √1520, which is approximately 39.
Therefore, the square root of (1476 + 44) is approximately ±39.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1476 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 156.84 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1476 + 40) = 2 × (38.42 + 40) = 2 × 78.42 = 156.84 units.
FAQ on Square Root of 1476
1.What is √1476 in its simplest form?
2.Mention the factors of 1476.
3.Calculate the square of 1476.
4.Is 1476 a prime number?
5.1476 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1476?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1476?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1476
- 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 is more commonly used due to its relevance in the real world. This is known as the principal square root.
- Factors: Factors are numbers that divide a given number completely without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
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Jaskaran Singh Saluja
About the Author
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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