Square Root of 1020
2026-02-28 13:58 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 a square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1020.

What is the Square Root of 1020?

The square root is the inverse of the square of the number. 1020 is not a perfect square. The square root of 1020 is expressed in both radical and exponential form. In the radical form, it is expressed as √1020, whereas (1020)^(1/2) in the exponential form. √1020 ≈ 31.951, 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 1020

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers, where long division and approximation methods are more suitable. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 1020 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1020 is broken down into its prime factors.

Step 1: Finding the prime factors of 1020. Breaking it down, we get 2 x 2 x 3 x 5 x 17: 2² x 3¹ x 5¹ x 17¹.

Step 2: Now we have found the prime factors of 1020. The second step is to make pairs of those prime factors. Since 1020 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating √1020 using prime factorization directly is not feasible.

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Square Root of 1020 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square numbers around 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 1020, we need to group it as 20 and 10.

Step 2: Now we need to find a number whose square is less than or equal to 10. We can say n is ‘3’ because 3 x 3 = 9, which is less than 10. Now the quotient is 3; after subtracting 9 from 10, the remainder is 1.

Step 3: Bring down 20, making the new dividend 120. Double the old divisor (3) to get 6, which will be the start of our new divisor.

Step 4: Now we need to find a digit n such that 6n x n is less than or equal to 120. n here is 1, as 61 x 1 = 61.

Step 5: Subtract 61 from 120 to get 59. 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. The new dividend is 5900.

Step 6: Now we need to find the new divisor, which is 639, because when multiplied by 9, gives a product less than or equal to 5900.

Step 7: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √1020 is approximately 31.95.

Square Root of 1020 by Approximation Method

The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 1020 using the approximation method.

Step 1: Find the closest perfect squares around √1020. The smallest perfect square less than 1020 is 961 (31²) and the largest perfect square greater than 1020 is 1024 (32²). √1020 falls somewhere between 31 and 32.

Step 2: Now apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1020 - 961) ÷ (1024 - 961) = 59/63 ≈ 0.937. Using this formula, we identified the decimal point of our square root.

The next step is adding the integer part to the decimal number, which is 31 + 0.937 ≈ 31.937.

Common Mistakes and How to Avoid Them in the Square Root of 1020

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few common mistakes students 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 √1020?

Okay, lets begin

The area of the square is 1020 square units.

Explanation

The area of the square = side².

The side length is given as √1020.

Area of the square = side²

= √1020 x √1020

= 1020.

Therefore, the area of the square box is 1020 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1020 square feet is built; if each of the sides is √1020, what will be the square feet of half of the building?

Okay, lets begin

510 square feet

Explanation

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

Dividing 1020 by 2, we get 510.

So half of the building measures 510 square feet.

Well explained 👍

Problem 3

Calculate √1020 x 5.

Okay, lets begin

159.755

Explanation

The first step is to find the square root of 1020, which is approximately 31.951.

The second step is to multiply 31.951 by 5.

So, 31.951 x 5 ≈ 159.755.

Well explained 👍

Problem 4

What will be the square root of (1000 + 20)?

Okay, lets begin

The square root is approximately 31.951.

Explanation

To find the square root, we need to find the sum of (1000 + 20) = 1020. Then the square root of 1020 is approximately 31.951.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √1020 units and the width ‘w’ is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 143.902 units.

Explanation

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

Perimeter = 2 × (√1020 + 40)

= 2 × (31.951 + 40)

= 2 × 71.951

≈ 143.902 units.

Well explained 👍

FAQ on Square Root of 1020

1.What is √1020 in its simplest form?

The prime factorization of 1020 is 2 x 2 x 3 x 5 x 17, so the simplest form of √1020 = √(2² x 3 x 5 x 17).

2.Mention the factors of 1020.

Factors of 1020 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 85, 102, 170, 204, 255, 340, 510, and 1020.

3.Calculate the square of 1020.

We get the square of 1020 by multiplying the number by itself, that is 1020 x 1020 = 1,040,400.

4.Is 1020 a prime number?

1020 is not a prime number, as it has more than two factors.

5.1020 is divisible by?

1020 has many factors, including 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 85, 102, 170, 204, 255, 340, 510, and 1020.

Important Glossaries for the Square Root of 1020

  • Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse of the square is the square root: √16 = 4.
     
  • Irrational number: An irrational number 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, the positive square root is the one most often used in practical applications, known as the principal square root.
     
  • Prime factorization: The process of breaking down a composite number into its prime factors.
     
  • Decimal: A number that has a whole number and a fractional part, separated by a decimal point, e.g., 7.86, 8.65, 9.42.

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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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