121 LearnersLast updated on May 26th, 2025
Square Root of 34.96
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 34.96.
What is the Square Root of 34.96?
The square root is the inverse of the square of the number. 34.96 is not a perfect square. The square root of 34.96 is expressed in both radical and exponential form. In the radical form, it is expressed as √34.96, whereas (34.96)^(1/2) in the exponential form. √34.96 = 5.912, which is a rational number because it can be expressed as a fraction.
Finding the Square Root of 34.96
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 34.96 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 34.96 is broken down into its prime factors:
Step 1: Convert 34.96 to a fraction, which is 3496/100.
Step 2: Find the prime factors of both the numerator and the denominator.
- Prime factors of 3496 are 2 x 2 x 2 x 2 x 3 x 73.
- Prime factors of 100 are 2 x 2 x 5 x 5.
Step 3: Since 34.96 is not a perfect square, finding the exact square root using prime factorization is complex.
Square Root of 34.96 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.
Step 1: Group the numbers from right to left. Here, we treat it as 34.96.
Step 2: Find the largest number whose square is less than or equal to 34. The number is 5 (since 5 x 5 = 25).
Step 3: Subtract 25 from 34, giving a remainder of 9. Bring down 96, making it 996.
Step 4: Double the current quotient (5), which is 10. Now find a digit (n) such that 10n x n ≤ 996. The digit is 9 (since 109 x 9 = 981).
Step 5: Subtract 981 from 996, leaving a remainder of 15. Add decimal points and two zeros, making it 1500.
Step 6: Repeat this process to get the decimal places.
Continuing yields a quotient of 5.912.
Square Root of 34.96 by Approximation Method
The approximation method is another method for finding the 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 34.96 using the approximation method.
Step 1: Identify the closest perfect squares around 34.96. The closest perfect squares are 25 (5^2) and 36 (6^2).
Step 2: Since 34.96 is closer to 36 than to 25, we approximate the square root to be slightly less than 6.
Step 3: By checking between 5.9 and 6, we find the square root of 34.96 is approximately 5.912.
Common Mistakes and How to Avoid Them in the Square Root of 34.96
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 usually consider only the positive square root, as it is the required one.
For example, √34.96 = 5.912, but there is also -5.912, which should not be forgotten.
Square Root of 34.96 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √34.96?
The area of the square is 34.96 square units.
Explanation
The area of the square = side^2.
The side length is given as √34.96.
Area of the square = side^2 = √34.96 x √34.96 = 5.912 x 5.912 = 34.96.
Therefore, the area of the square box is 34.96 square units.
Problem 2
A square-shaped building measuring 34.96 square feet is built; if each of the sides is √34.96, what will be the square feet of half of the building?
17.48 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 34.96 by 2 = we get 17.48.
So half of the building measures 17.48 square feet.
Problem 3
Calculate √34.96 x 4.
23.648
Explanation
The first step is to find the square root of 34.96, which is 5.912.
The second step is to multiply 5.912 by 4. So 5.912 x 4 = 23.648.
Problem 4
What will be the square root of (30 + 4.96)?
The square root is 5.912
Explanation
To find the square root, we need to find the sum of (30 + 4.96). 30 + 4.96 = 34.96, and then √34.96 = 5.912.
Therefore, the square root of (30 + 4.96) is ±5.912.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √34.96 units and the width ‘w’ is 5 units.
We find the perimeter of the rectangle as 21.824 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√34.96 + 5) = 2 × (5.912 + 5) = 2 × 10.912 = 21.824 units.
FAQ on Square Root of 34.96
1.What is √34.96 in its simplest form?
2.Mention the factors of 34.96.
3.Calculate the square of 34.96.
4.Is 34.96 a prime number?
5.34.96 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 34.96?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 34.96?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 34.96
- 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.
- Rational number: A rational number is a number that can 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, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Decimals: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.
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About BrightChamps in Vietnam
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.
