101 LearnersLast updated on May 26th, 2025
Square Root of 3.52
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 3.52.
What is the Square Root of 3.52?
The square root is the inverse of the square of the number. 3.52 is not a perfect square. The square root of 3.52 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.52, whereas (3.52)^(1/2) in the exponential form. √3.52 ≈ 1.876, 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 3.52
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 3.52 by Prime Factorization Method
The prime factorization method involves expressing the number as a product of prime factors. However, 3.52 is not a perfect square, and its decimal form complicates direct prime factorization. Thus, this method is not suitable for 3.52.
Square Root of 3.52 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: Start with the number 3.52. We can consider it as 352/100 for simplification purposes.
Step 2: Find the largest number whose square is less than or equal to 3. We find that 1 is the largest number, as 1 × 1 = 1.
Step 3: Subtract 1 from 3 to get the remainder 2. Bring down 5 to make it 25.
Step 4: Double 1 (the previous quotient) to get 2. Now, find a number 'n' such that 2n × n ≤ 25. We find n = 1, as 21 × 1 = 21.
Step 5: Subtract 21 from 25 to get the remainder 4. Bring down 2 to make it 42.
Step 6: Double 11 to get 22. Find 'n' such that 22n × n ≤ 42, which gives n = 1.
Step 7: Subtract 22 from 42 to get 20.
Step 8: Add a decimal point and bring down 00 to make it 2000.
Step 9: Repeat the process to find more decimal places as needed.
The quotient so far is approximately 1.876 when rounded to three decimal places.
Square Root of 3.52 by Approximation Method
Approximation method is another method for finding the square roots. It is a simple method to estimate the square root of a given number. Now let us learn how to find the square root of 3.52 using the approximation method.
Step 1: Identify the nearest perfect squares around 3.52. The nearest perfect square below 3.52 is 1 (√1 = 1), and the nearest above is 4 (√4 = 2).
Step 2: Since 3.52 is closer to 4 than to 1, we approximate √3.52 to be closer to 2.
Step 3: Using the linear approximation formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). For 3.52, approximate √3.52 ≈ 1.876.
This approximation gives a close estimate of the square root of 3.52.
Common Mistakes and How to Avoid Them in the Square Root of 3.52
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root for practical applications.
For example, √3.52 ≈ ±1.876, but we usually use the positive value.
Square root of 3.52 Examples
Problem 1
Can you help Anna find the area of a square box if its side length is given as √3.52?
The area of the square is approximately 3.52 square units.
Explanation
The area of the square = side².
The side length is given as √3.52.
Area of the square = (√3.52)² = 3.52.
Therefore, the area of the square box is approximately 3.52 square units.
Problem 2
A square-shaped garden measuring 3.52 square meters is built; if each of the sides is √3.52, what will be the square meters of half of the garden?
1.76 square meters
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 3.52 by 2, we get 1.76.
So half of the garden measures 1.76 square meters.
Problem 3
Calculate √3.52 × 5.
Approximately 9.38
Explanation
The first step is to find the square root of 3.52, which is approximately 1.876.
The second step is to multiply 1.876 by 5. So 1.876 × 5 ≈ 9.38.
Problem 4
What will be the square root of (3 + 0.52)?
The square root is approximately 1.876.
Explanation
To find the square root, we need to find the sum of (3 + 0.52). 3 + 0.52 = 3.52, and then √3.52 ≈ 1.876.
Therefore, the square root of (3 + 0.52) is approximately ±1.876.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √3.52 units and the width ‘w’ is 2 units.
We find the perimeter of the rectangle as approximately 7.752 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3.52 + 2) ≈ 2 × (1.876 + 2) ≈ 2 × 3.876 ≈ 7.752 units.
FAQ on Square Root of 3.52
1.What is √3.52 in its simplest form?
2.Can 3.52 be expressed as a product of prime factors?
3.Calculate the square of 3.52.
4.Is 3.52 a perfect square?
5.What is the decimal approximation of the square root of 3.52?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 3.52?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 3.52?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 3.52
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which is √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 typically used in practical scenarios and is known as the principal square root.
- Decimal: A number that includes a whole number and a fraction expressed in a single form, such as 7.86, 8.65, and 9.42, is a decimal.
- Long division method: A step-by-step approach to finding the square root of a number by dividing and estimating the quotient systematically.
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Jaskaran Singh Saluja
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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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