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464 LearnersLast updated on August 5, 2025
Square Root of 3.2
What is the Square Root of 3.2?
The square root is the inverse of the square of the number. 3.2 is not a perfect square. The square root of 3.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.2, whereas (3.2)^(1/2) in the exponential form. √3.2 ≈ 1.78885, 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 3.2
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 3.2 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, since 3.2 is not an integer, it cannot be broken down into prime factors using the traditional method applicable to whole numbers. Therefore, calculating the square root of 3.2 using prime factorization is not feasible.
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Square Root of 3.2 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, we need to consider 3.2 as 32/10.
Step 2: Find the closest perfect square to 3.2. Here, the closest perfect square is 1.
Step 3: Divide and adjust using decimal places as needed.
Step 4: Continue the division process to gain precision, using decimal places to ensure accuracy.
Square Root of 3.2 by Approximation Method
The approximation method is another method for finding square roots and is an easy way to estimate the square root of a given number. Now let us learn how to find the square root of 3.2 using the approximation method.
Step 1: Now we have to find the closest perfect squares around 3.2. The closest perfect squares are 1 (1^2 = 1) and 4 (2^2 = 4). Thus, √3.2 falls between 1 and 2.
Step 2: Use interpolation to approximate more precisely if needed. Given that 3.2 is closer to 4 than to 1, we can estimate that √3.2 is approximately 1.78885.
Common Mistakes and How to Avoid Them in the Square Root of 3.2
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root for practical applications.
For example, √50 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Misplacing the square root symbol is a common mistake. We need to teach students that simplifying numbers inside the square root is crucial before moving on to further calculations.
For example, √(12 + 24) = √36 is correct, whereas √12 + √24 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid errors when identifying the approximate value.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots to avoid confusion.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, and students might skip a step accidentally, resulting in an incorrect answer. This may happen during subtraction or elsewhere in the process.
Square Root of 3.2 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3.2?
The area of the square is approximately 3.2 square units.
Explanation
The area of a square = side^2.
The side length is given as √3.2.
Area of the square = (√3.2)^2 = 3.2.
Therefore, the area of the square box is approximately 3.2 square units.
Problem 2
A square-shaped garden measures 3.2 square meters in area. If each side is √3.2, what is the area of half of the garden?
1.6 square meters
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 3.2 by 2 gives us 1.6.
So half of the garden measures 1.6 square meters.
Problem 3
Calculate √3.2 × 5.
Approximately 8.94425
Explanation
First, find the square root of 3.2, which is approximately 1.78885.
Then multiply 1.78885 by 5.
So, 1.78885 × 5 ≈ 8.94425.
Problem 4
What will be the square root of (2.2 + 1)?
The square root is approximately 2.
Explanation
To find the square root, first find the sum of 2.2 + 1 = 3.2.
Then, √3.2 ≈ 1.78885.
Therefore, the square root of (2.2 + 1) is approximately ±1.78885.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √3.2 units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 13.5777 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√3.2 + 5) ≈ 2 × (1.78885 + 5) ≈ 2 × 6.78885 ≈ 13.5777 units.
FAQ on Square Root of 3.2
1.What is √3.2 in its simplest form?
2.Is 3.2 a perfect square?
3.Calculate the square of 3.2.
4.Is 3.2 a rational number?
5.What are the closest whole numbers that √3.2 lies between?
Important Glossaries for the Square Root of 3.2
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Rational number: A number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
- Decimal: A number that has a whole number and a fraction in a single number, such as 3.2 or 7.86.
- Approximation: A value or number that is close to but not exactly equal to the actual value, often used when the exact value is difficult to obtain.
Vikrant Sharma
About the Author
Vikrant is a passionate Mathematics teacher with over 5 years of teaching experience in both conventional and Vedic Maths. His student-focused approach combines clear concepts with motivation and encouragement, helping students build confidence and develo
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
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