105 LearnersLast updated on May 26th, 2025
Square Root of 1404
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 1404.
What is the Square Root of 1404?
The square root is the inverse of the square of the number. 1404 is not a perfect square. The square root of 1404 is expressed in both radical and exponential form. In radical form, it is expressed as √1404, whereas in exponential form it is (1404)^(1/2). √1404 ≈ 37.478, 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 1404
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are often used. Let us now learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1404 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1404 is broken down into its prime factors:
Step 1: Finding the prime factors of 1404 Breaking it down, we get 2 x 2 x 3 x 3 x 3 x 13.
Step 2: Now that we have found the prime factors of 1404, the next step is to make pairs of these prime factors. Since 1404 is not a perfect square, the digits of the number cannot be grouped into pairs completely.
Therefore, calculating √1404 using prime factorization requires approximation.
Square Root of 1404 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 1404, we need to group it as 14 and 04.
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: Bring down 04, making the new dividend 504. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find n such that 6n × n ≤ 504. Let us consider n as 8. Now, 68 x 8 = 544.
Step 5: Since 544 is greater than 504, we try n as 7. So, 67 x 7 = 469, which is less than 504.
Step 6: Subtract 469 from 504. The difference is 35, and the quotient is 37.
Step 7: Since the remaining dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 3500.
Step 8: Find the new divisor: 746 x 4 = 2984.
Step 9: Subtracting 2984 from 3500 gives 516.
Step 10: The quotient is now 37.4.
Step 11: Continue doing these steps until we achieve the desired level of precision.
Thus, the square root of √1404 is approximately 37.48.
Square Root of 1404 by Approximation Method
The approximation method is another approach for finding square roots, and it is an easy method to estimate the square root of a given number. Let us learn how to find the square root of 1404 using the approximation method.
Step 1: We have to find the closest perfect squares of √1404.
The smallest perfect square less than 1404 is 1369 (37^2) and the largest perfect square greater than 1404 is 1444 (38^2). Therefore, √1404 falls between 37 and 38.
Step 2: Now we need to apply the formula: (Given number - Smaller perfect square) / (Larger perfect square - Smaller perfect square).
Using this formula, (1404 - 1369) / (1444 - 1369) = 35 / 75 ≈ 0.467. Adding this value to the smaller base value we found gives 37 + 0.467 ≈ 37.467.
Hence, the square root of 1404 is approximately 37.467.
Common Mistakes and How to Avoid Them in the Square Root of 1404
Students often make mistakes while finding the square root, such as forgetting the negative square root or skipping steps in the long division method. Let's look at a few common mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we typically take only the positive square root as it is the one most often used in practical applications.
For example, √50 = 7.071, but there is also -7.071, which should not be forgotten.
Square Root of 1404 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1404?
The area of the square is approximately 1404 square units.
Explanation
The area of a square is side^2.
The side length is given as √1404.
Area of the square = side^2 = √1404 × √1404 = 1404.
Therefore, the area of the square box is approximately 1404 square units.
Problem 2
A square-shaped building measuring 1404 square feet is built. If each of the sides is √1404, what will be the square feet of half of the building?
702 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1404 by 2, we get 702.
So, half of the building measures 702 square feet.
Problem 3
Calculate √1404 × 5.
Approximately 187.39
Explanation
First, find the square root of 1404, which is approximately 37.48.
Then, multiply 37.48 by 5.
So, 37.48 × 5 ≈ 187.39.
Problem 4
What will be the square root of (1400 + 4)?
The square root is approximately 37.48
Explanation
To find the square root, we need to find the sum of (1400 + 4), which is 1404.
The square root of 1404 is approximately 37.48.
Therefore, the square root of (1400 + 4) is approximately ±37.48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1404 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 150.96 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1404 + 38) = 2 × (37.48 + 38) = 2 × 75.48 = 150.96 units.
FAQ on Square Root of 1404
1.What is √1404 in its simplest form?
2.Mention the factors of 1404.
3.Calculate the square of 1404.
4.Is 1404 a prime number?
5.1404 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 1404?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1404?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1404
- Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 x 4 = 16.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0. Examples include √2 and π.
- Principal square root: The principal square root of a non-negative number is its non-negative square root. For example, the principal square root of 9 is 3.
- Prime factorization: This is the expression of a number as the product of its prime numbers. For example, the prime factorization of 28 is 2 x 2 x 7.
- Approximation method: This method is used to estimate values, such as square roots, by finding the nearest known values and interpolating between them.
Explore More algebra
Previous to Square Root of 1404
About BrightChamps in Australia
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
