Square Root of 1.48
2026-02-28 13:09 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1.48

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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, etc. Here, we will discuss the square root of 1.48.

What is the Square Root of 1.48?

The square root is the inverse of the square of the number. 1.48 is not a perfect square. The square root of 1.48 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.48, whereas (1.48)^(1/2) in the exponential form. √1.48 ≈ 1.21655, 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 1.48

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 1.48 by Prime Factorization Method

Prime factorization is the process of expressing a number as the product of its prime factors. Since 1.48 is not a perfect square, it cannot be represented through integer prime factorization. Therefore, calculating the square root of 1.48 using prime factorization is impractical.

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Square Root of 1.48 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we find the square root step by step by considering pairs of digits from the decimal point.

Step 1: To begin with, we need to group the number. For 1.48, we consider it as 1.48 since it's a decimal number.

Step 2: Find a number 'n' such that n² ≤ 1. The number is 1 because 1² = 1.

Step 3: Subtract 1 from 1, bringing down 48, which results in 48 as the new dividend.

Step 4: Double the number in the quotient (which is 1), making it 2. Find a digit 'd' such that 2d × d ≤ 48. The digit is 2 since 22 × 2 = 44.

Step 5: Subtract 44 from 48, yielding a remainder of 4. Bring down two zeroes, making the new dividend 400.

Step 6: Repeat the process to find the next digits. Continue this process to get more decimal places.

The square root of 1.48 is approximately 1.21655.

Square Root of 1.48 by Approximation Method

Approximation is an easier method to find the square root of a given number.

Step 1: Identify two consecutive perfect squares between which 1.48 lies. The closest perfect squares are 1 (1²) and 4 (2²). √1.48 falls between 1 and 2.

Step 2: Using interpolation, we can estimate the value more precisely.

By estimating, we find that √1.48 is approximately 1.21655.

Common Mistakes and How to Avoid Them in the Square Root of 1.48

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. Let us explore these common errors in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √1.48?

Okay, lets begin

The area of the square is approximately 1.4808 square units.

Explanation

The area of a square is given by side².

The side length is √1.48.

Area of the square = (√1.48)² = 1.48.

Therefore, the area of the square box is approximately 1.48 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1.48 square feet is built; if each of the sides is √1.48, what will be the square feet of half of the building?

Okay, lets begin

0.74 square feet

Explanation

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

Dividing 1.48 by 2 = 0.74

So half of the building measures 0.74 square feet.

Well explained 👍

Problem 3

Calculate √1.48 x 5.

Okay, lets begin

Approximately 6.08275

Explanation

First, find the square root of 1.48, which is approximately 1.21655.

Then multiply 1.21655 by 5.

So, 1.21655 x 5 ≈ 6.08275.

Well explained 👍

Problem 4

What will be the square root of (1.48 + 0.52)?

Okay, lets begin

The square root is 1.414

Explanation

To find the square root, calculate the sum of (1.48 + 0.52). 1.48 + 0.52 = 2, and then √2 ≈ 1.414.

Therefore, the square root of (1.48 + 0.52) is approximately ±1.414.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1.48 units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 8.4331 units.

Explanation

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

Perimeter = 2 × (√1.48 + 3) ≈ 2 × (1.21655 + 3)

= 2 × 4.21655

≈ 8.4331 units.

Well explained 👍

FAQ on Square Root of 1.48

1.What is √1.48 in its simplest form?

The simplest form of √1.48 is just its decimal approximation, which is approximately 1.21655, since 1.48 cannot be simplified into smaller integer factors under a square root.

2.What are the factors of 1.48?

The factors of 1.48 are 1, 0.74, and 1.48, considering its decimal nature.

3.Calculate the square of 1.48.

The square of 1.48 is obtained by multiplying the number by itself: 1.48 x 1.48 = 2.1904.

4.Is 1.48 a prime number?

5.Is 1.48 divisible by any integers?

1.48 can be divided by integers like 1 and 2, but it results in non-integers.

Important Glossaries for the Square Root of 1.48

  • Square Root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, √4 = 2 because 2² = 4.
     
  • Irrational Number: An irrational number cannot be expressed as a simple fraction. Examples include √2 and π.
     
  • Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 3.14.
     
  • Perfect Square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4².
     
  • Long Division Method: A technique used to find the square root of a number by systematically dividing and subtracting to reach a close approximation.

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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.