Square Root of 1.3
2026-02-28 08:18 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 such as vehicle design, finance, and more. Here, we will discuss the square root of 1.3.

What is the Square Root of 1.3?

The square root is the inverse of the square of a number. 1.3 is not a perfect square. The square root of 1.3 can be expressed in both radical and exponential forms. In radical form, it is expressed as √1.3, whereas it is expressed as (1.3)^(1/2) in exponential form. √1.3 ≈ 1.140175, 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 1.3

The prime factorization method is used for perfect square numbers. However, this method is not applicable for non-perfect squares like 1.3, where methods such as long division and approximation are used. Let us learn the following methods:

  • Long division method
     
  • Approximation method

Square Root of 1.3 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Begin by grouping the numbers from right to left. For 1.3, consider it as 1.30.

Step 2: Find n whose square is less than or equal to 1. We can use n = 1 since 1 × 1 = 1. Subtract 1 from 1 to get a remainder of 0, and bring down 30 to make the new dividend 30.

Step 3: Double the divisor (1), which becomes 2, and use it as the new divisor.

Step 4: Find a digit 'd' such that 2d × d is less than or equal to 30. We find d = 1 because 21 × 1 = 21 is less than 30.

Step 5: Subtract 21 from 30 to get a remainder of 9 and bring down 00 to make the new dividend 900.

Step 6: The new divisor becomes 22 (by adding 1 to 21). Find a digit 'd' such that 22d × d is less than or equal to 900. We find d = 4 because 224 × 4 = 896.

Step 7: Continue this process to get the square root to the desired precision.

The square root of 1.3 is approximately 1.14.

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Square Root of 1.3 by Approximation Method

The approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 1.3 using the approximation method.

Step 1: Identify the closest perfect squares to 1.3. The closest perfect squares are 1 (1^2) and 1.44 (1.2^2). Therefore, √1.3 lies between 1 and 1.2.

Step 2: Apply the approximation formula: (Given number - smaller perfect square) ÷ (Larger perfect square - smaller perfect square). Using the formula: (1.3 - 1) ÷ (1.44 - 1) ≈ 0.6818.

Step 3: Add this decimal to the smaller square root: 1 + 0.6818 ≈ 1.14.

Therefore, the square root of 1.3 is approximately 1.14.

Common Mistakes and How to Avoid Them in the Square Root of 1.3

Students often make mistakes while finding the square root, such as ignoring negative square roots, skipping steps in the long division method, etc. Let's discuss a few common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √1.3?

Okay, lets begin

The area of the square is approximately 1.3 square units.

Explanation

The area of a square = side².

The side length is given as √1.3.

Area of the square = (√1.3)² = 1.3.

Therefore, the area of the square box is approximately 1.3 square units.

Well explained 👍

Problem 2

A square-shaped plot measuring 1.3 square meters is built; if each of the sides is √1.3, what will be the area of half of the plot?

Okay, lets begin

0.65 square meters

Explanation

We can just divide the given area by 2 since the plot is square-shaped.

Dividing 1.3 by 2 = 0.65

Hence, half of the plot measures 0.65 square meters.

Well explained 👍

Problem 3

Calculate √1.3 × 5.

Okay, lets begin

Approximately 5.701

Explanation

The first step is to find the square root of 1.3, which is approximately 1.14.

The second step is to multiply 1.14 by 5. So, 1.14 × 5 ≈ 5.701.

Well explained 👍

Problem 4

What will be the square root of (1 + 0.3)?

Okay, lets begin

Approximately 1.14

Explanation

To find the square root, we calculate (1 + 0.3) = 1.3, and then √1.3 ≈ 1.14.

Therefore, the square root of (1 + 0.3) is approximately ±1.14.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √1.3 units and the width 'w' is 3 units.

Okay, lets begin

The perimeter of the rectangle is approximately 8.28 units.

Explanation

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

Perimeter = 2 × (√1.3 + 3) ≈ 2 × (1.14 + 3) ≈ 2 × 4.14 = 8.28 units.

Well explained 👍

FAQ on Square Root of 1.3

1.What is √1.3 in its simplest form?

Since 1.3 is not a perfect square, its simplest radical form remains √1.3.

2.What are the factors of 1.3?

Factors of 1.3, a decimal, are not typically listed like whole numbers. However, it can be expressed as a fraction 13/10, and its factors are related to the numbers 13 and 10.

3.Calculate the square of 1.3.

The square of 1.3 is calculated by multiplying the number by itself: 1.3 × 1.3 = 1.69.

4.Is 1.3 a prime number?

5.Is 1.3 divisible by any integers?

1.3 can be divided by integers, but the result will be a decimal. For instance, 1.3 ÷ 1 = 1.3, and 1.3 ÷ 2 = 0.65.

Important Glossaries for the Square Root of 1.3

  • Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16, and the inverse is √16 = 4.
  • Irrational number: An irrational number cannot be written in the form p/q, where q ≠ 0 and p and q are integers. Example: √1.3.
  • Principal square root: The positive square root of a number is called the principal square root, often used in practical applications.
  • Decimal: A numerical representation that includes a whole number and a fractional part separated by a decimal point, such as 1.3.
  • Long division method: A step-by-step approach to finding the square root of non-perfect squares, involving 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.