Square Root of 1764
2026-02-28 08:22 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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 1764.

What is the Square Root of 1764?

The square root is the inverse of the square of the number. 1764 is a perfect square. The square root of 1764 is expressed in both radical and exponential form. In the radical form, it is expressed as √1764, whereas (1764)^(1/2) in the exponential form. √1764 = 42, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 1764

The prime factorization method is used for perfect square numbers. 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 1764 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1764 is broken down into its prime factors.

Step 1: Finding the prime factors of 1764 Breaking it down, we get 2 x 2 x 3 x 3 x 7 x 7: 2^2 x 3^2 x 7^2

Step 2: Now we found out the prime factors of 1764. The second step is to make pairs of those prime factors. Since 1764 is a perfect square, we can group the digits of the number in pairs.

Therefore, calculating the square root of 1764 using prime factorization is possible. The square root is 2 x 3 x 7 = 42.

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Square Root of 1764 by Long Division Method

The long division method is particularly used for 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 1764, we need to group it as 64 and 17.

Step 2: Now we need to find n whose square is less than or equal to 17. We can choose n as 4 because 4 x 4 = 16 is less than 17. Now the quotient is 4, and after subtracting, the remainder is 1.

Step 3: Bring down 64, making the new dividend 164. Add the old divisor with the same number, 4 + 4, to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n such that 8n x n ≤ 164. Let us consider n as 2, now 82 x 2 = 164.

Step 5: Subtract 164 from 164, and the remainder is 0. The quotient is 42.

Therefore, the square root of 1764 is 42.

Square Root of 1764 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 1764 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1764. The smallest perfect square before 1764 is 1600, and the largest perfect square is 1764. √1764 is exactly 42.

Step 2: Since 1764 is a perfect square, no further approximation is needed.

The square root of 1764 is 42.

Common Mistakes and How to Avoid Them in the Square Root of 1764

Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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 √1444?

Okay, lets begin

The area of the square is 1444 square units.

Explanation

The area of the square = side^2.

The side length is given as √1444.

Area of the square = side^2 = √1444 x √1444 = 38 × 38 = 1444.

Therefore, the area of the square box is 1444 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1764 square feet is built; if each of the sides is √1764, what will be the square feet of half of the building?

Okay, lets begin

882 square feet

Explanation

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

Dividing 1764 by 2 = we get 882.

So half of the building measures 882 square feet.

Well explained 👍

Problem 3

Calculate √1764 x 5.

Okay, lets begin

210

Explanation

The first step is to find the square root of 1764, which is 42.

The second step is to multiply 42 with 5. So 42 x 5 = 210.

Well explained 👍

Problem 4

What will be the square root of (1600 + 64)?

Okay, lets begin

The square root is 42.

Explanation

To find the square root, we need to find the sum of (1600 + 64).

1600 + 64 = 1664, and then 1664 is not a perfect square, so we need to find the approximate value.

However, 1764 is 1600 + 164, which is a perfect square.

Therefore, the square root of (1600 + 64) is 42.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1444 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 152 units.

Explanation

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

Perimeter = 2 × (√1444 + 38) = 2 × (38 + 38) = 2 × 76 = 152 units.

Well explained 👍

FAQ on Square Root of 1764

1.What is √1764 in its simplest form?

The prime factorization of 1764 is 2 x 2 x 3 x 3 x 7 x 7, so the simplest form of √1764 = √(2^2 x 3^2 x 7^2) = 42.

2.Mention the factors of 1764.

Factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 294, 441, 588, 882, and 1764.

3.Calculate the square of 1764.

We get the square of 1764 by multiplying the number by itself, that is 1764 x 1764 = 3,111,696.

4.Is 1764 a prime number?

1764 is not a prime number, as it has more than two factors.

5.1764 is divisible by?

1764 has many factors; those are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 294, 441, 588, 882, and 1764.

Important Glossaries for the Square Root of 1764

  • Square root: A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root, that is √36 = 6.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because it is 7^2.
  • Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
  • Dividend: A dividend is a number that is being divided by another number in a division operation.

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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.