Square Root of 1496
2026-02-21 20:26 Diff
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Last updated on August 5, 2025

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 1496.

What is the Square Root of 1496?

The square root is the inverse of the square of the number. 1496 is not a perfect square. The square root of 1496 is expressed in both radical and exponential form. In the radical form, it is expressed as √1496, whereas (1496)^(1/2) in exponential form. √1496 ≈ 38.6709, 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 1496

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 1496 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1496 is broken down into its prime factors:

Step 1: Finding the prime factors of 1496 Breaking it down, we get 2 x 2 x 2 x 11 x 17: 2^3 x 11 x 17

Step 2: Now we found out the prime factors of 1496. The second step is to make pairs of those prime factors. Since 1496 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1496 using prime factorization is impossible.

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Square Root of 1496 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 1496, we need to group it as 96 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 14. Now the quotient is 3. After subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 96, which is the new dividend. 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 the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 596. Let us consider n as 8, now 68 × 8 = 544.

Step 6: Subtract 596 from 544; the difference is 52, 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 5200.

Step 8: Now we need to find the new divisor for which we add a digit to 76. Find a number such that when it multiplies with the number formed, it is less than or equal to 5200.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √1496 is approximately 38.6709.

Square Root of 1496 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 1496 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1496.

The smallest perfect square less than 1496 is 1444, and the largest perfect square greater than 1496 is 1521. √1496 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 (1496 - 1444) ÷ (1521 - 1444) = 52 ÷ 77 ≈ 0.6753.

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 38 + 0.6753 ≈ 38.6753.

So the square root of 1496 is approximately 38.6753.

Common Mistakes and How to Avoid Them in the Square Root of 1496

Students do make mistakes while finding the square root, like forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1496?

Okay, lets begin

The area of the square is 1496 square units.

Explanation

The area of the square = side².

The side length is given as √1496.

Area of the square = side² = √1496 x √1496 = 1496.

Therefore, the area of the square box is 1496 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1496 square feet is built; if each of the sides is √1496, what will be the square feet of half of the building?

Okay, lets begin

748 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 1496 by 2 = we get 748.

So half of the building measures 748 square feet.

Well explained 👍

Problem 3

Calculate √1496 x 5.

Okay, lets begin

193.3545

Explanation

The first step is to find the square root of 1496, which is approximately 38.6709.

The second step is to multiply 38.6709 by 5.

So 38.6709 x 5 ≈ 193.3545.

Well explained 👍

Problem 4

What will be the square root of (1456 + 40)?

Okay, lets begin

The square root is 40.

Explanation

To find the square root, we need to find the sum of (1456 + 40). 1456 + 40 = 1496, and then √1496 ≈ 38.6709.

Therefore, the square root of (1456 + 40) is approximately ±38.6709.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1496 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 153.3418 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√1496 + 38) = 2 × (38.6709 + 38) ≈ 2 × 76.6709 ≈ 153.3418 units.

Well explained 👍

FAQ on Square Root of 1496

1.What is √1496 in its simplest form?

The prime factorization of 1496 is 2 x 2 x 2 x 11 x 17, so the simplest form of √1496 = √(2 x 2 x 2 x 11 x 17).

2.Mention the factors of 1496.

Factors of 1496 are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.

3.Calculate the square of 1496.

We get the square of 1496 by multiplying the number by itself, that is 1496 x 1496 = 2,238,016.

4.Is 1496 a prime number?

1496 is not a prime number, as it has more than two factors.

5.1496 is divisible by?

1496 has many factors; those are 1, 2, 4, 8, 11, 17, 22, 34, 44, 68, 88, 136, 187, 272, 374, 748, and 1496.

Important Glossaries for the Square Root of 1496

  • Square root: A square root is the inverse of a square. Example: 4² = 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. That is the reason it is also known as a principal square root.
  • Approximation method: A method used to find the square root of non-perfect squares by finding the nearest perfect squares and calculating a decimal approximation.
  • Long division method: A step-by-step method used to find the square root of non-perfect square numbers through repeated division and subtraction.

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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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.