Square Root of 33.3
2026-02-28 23:19 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the 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 33.3

What is the Square Root of 33.3?

The square root is the inverse of the square of a number. 33.3 is not a perfect square. The square root of 33.3 is expressed in both radical and exponential form. In the radical form, it is expressed as √33.3, whereas (33.3)¹/² in the exponential form. √33.3 ≈ 5.7717, 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 33.3

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not applied. Instead, methods such as the long-division method and the approximation method are used. Let us now learn these methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 33.3 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. However, since 33.3 is not a whole number, traditional prime factorization is not applicable directly. For decimal numbers, approximation methods are more suitable.

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Square Root of 33.3 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, consider the integer part of 33.3, which is 33. Pair 33 from right to left.

Step 2: Find a number whose square is less than or equal to 33. The number is 5, since 5 × 5 = 25.

Step 3: Subtract 25 from 33, we get a remainder of 8. Bring down two zeroes to make it 800.

Step 4: Double the quotient (5) and write it beside the divisor as 10. We need to find a digit x such that 10x × x is less than or equal to 800.

Step 5: By trial, 107 × 7 = 749.

Step 6: Subtract 749 from 800, we get 51. Bring down two more zeroes to make it 5100.

Step 7: Double the current quotient to get 114 and continue the process.

Step 8: Continue this process until the desired decimal places are reached.

So the square root of √33.3 ≈ 5.7717

Square Root of 33.3 by Approximation Method

The approximation method is another method for finding 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 33.3 using the approximation method.

Step 1: Now we have to find the closest perfect square of √33.3.

The closest perfect squares are 25 (5²) and 36 (6²).

√33.3 falls between 5 and 6.

Step 2: Now we apply the formula:

(Given number - smaller perfect square) / (larger perfect square - smaller perfect square)

Using the formula, (33.3 - 25) / (36 - 25) = 8.3 / 11 ≈ 0.7545

Adding this to 5: 5 + 0.7545 = 5.7545, so the square root of 33.3 ≈ 5.7717

Common Mistakes and How to Avoid Them in the Square Root of 33.3

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. Here are some common mistakes and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √33.3?

Okay, lets begin

The area of the square is approximately 33.3 square units.

Explanation

The area of the square = side².

The side length is given as √33.3.

Area of the square = side² = √33.3 × √33.3 = 33.3

Therefore, the area of the square box is approximately 33.3 square units.

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Problem 2

A square-shaped garden measures 33.3 square feet. If each side is √33.3, what is the length of each side?

Okay, lets begin

Each side of the garden is approximately 5.7717 feet.

Explanation

The side length of a square is the square root of its area.

So, if the area is 33.3 square feet, each side is √33.3 ≈ 5.7717 feet.

Well explained 👍

Problem 3

Calculate √33.3 × 5.

Okay, lets begin

Approximately 28.8585

Explanation

The first step is to find the square root of 33.3, which is approximately 5.7717.

The second step is to multiply 5.7717 by 5.

So, 5.7717 × 5 ≈ 28.8585.

Well explained 👍

Problem 4

What will be the square root of (25 + 8.3)?

Okay, lets begin

The square root is approximately 5.7717

Explanation

To find the square root, we need to find the sum of (25 + 8.3). 25 + 8.3 = 33.3, and then √33.3 ≈ 5.7717.

Therefore, the square root of (25 + 8.3) is approximately ±5.7717.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √33.3 units and the width ‘w’ is 10 units.

Okay, lets begin

The perimeter of the rectangle is approximately 31.5434 units.

Explanation

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

Perimeter = 2 × (√33.3 + 10) ≈ 2 × (5.7717 + 10) ≈ 2 × 15.7717 ≈ 31.5434 units.

Well explained 👍

FAQ on Square Root of 33.3

1.What is √33.3 in its simplest form?

As 33.3 is not a whole number, it does not have a simplest form in terms of radical simplification.

2.Is 33.3 a perfect square?

No, 33.3 is not a perfect square because it cannot be expressed as the square of an integer.

3.Calculate the square of 33.3.

To find the square of 33.3, multiply the number by itself: 33.3 × 33.3 ≈ 1108.89

4.Is 33.3 a prime number?

33.3 is not a prime number, as it is not an integer and cannot be evaluated in terms of prime factors.

5.What numbers is 33.3 divisible by?

33.3 is divisible by 1 and itself, but being a decimal, it is generally considered in contexts where division by integers is not straightforward.

Important Glossaries for the Square Root of 33.3

  • Square root: A square root is the inverse operation of squaring a number. For example, if 4² = 16, then √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.
     
  • Principal square root: The principal square root refers to the positive square root of a number. For example, the principal square root of 16 is 4.
     
  • Decimal: A decimal is a number expressed in the base-10 numeral system, which includes a whole number and a fractional part separated by a decimal point. For example, 33.3 is a decimal.
     
  • Long division method: A procedure used to find the square root of non-perfect squares by dividing and averaging to reach an 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.

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