102 LearnersLast updated on May 26th, 2025
Square Root of 4.9
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 4.9
What is the Square Root of 4.9?
The square root is the inverse of the square of the number. 4.9 is not a perfect square. The square root of 4.9 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.9, whereas (4.9)^(1/2) in the exponential form. √4.9 = 2.21359, 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 4.9
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 4.9 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4.9 is broken down into its prime factors.
Step 1: Converting 4.9 into a fraction, we have 49/10.
Step 2: Finding the prime factors of 49, we have 7 x 7.
Step 3: The prime factorization of 4.9 is (7 x 7) / (2 x 5).
The second step is to make pairs of those prime factors. Since 4.9 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating √4.9 using prime factorization is not straightforward.
Square Root of 4.9 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find the square root using a step-by-step approach.
Step 1: Start by placing a bar over 4 and 9 separately.
Step 2: Find a number whose square is less than or equal to 4. That number is 2 (since 2 x 2 = 4).
Step 3: Subtract 4 from 4, getting 0, and bring down 9.
Step 4: Double the quotient obtained, which is 2, to get 4.
Step 5: Find a number n such that 4n x n ≤ 90 (considering the next two decimal places).
Step 6: The closest number is 2 (since 42 x 2 = 84).
Step 7: Subtract 84 from 90 to get 6, and bring down two zeroes making it 600.
Step 8: The quotient now is 2.2.
Step 9: Repeat the process to get more decimal places if needed.
So the square root of √4.9 is approximately 2.213.
Square Root of 4.9 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 4.9 using the approximation method.
Step 1: Identify the closest perfect squares around 4.9.
The closest perfect squares are 4 (2) and 9 (3).
Step 2: √4.9 falls between √4 = 2 and √9 = 3.
Step 3: Use interpolation to estimate the value: (4.9 - 4) / (9 - 4) = 0.18
Step 4: Add this result to the smaller square root: 2 + 0.18 = 2.18
Thus, the approximate square root of 4.9 is 2.213.
Common Mistakes and How to Avoid Them in the Square Root of 4.9
Students make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in methods. Let's look at a few common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It is important to understand that a number has both positive and negative square roots. However, we typically consider only the positive square root in most practical applications.
For example, √4.9 ≈ 2.213, but there is also -2.213.
Square Root of 4.9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4.9?
The area of the square is 4.9 square units.
Explanation
The area of the square = side².
The side length is given as √4.9.
Area of the square = (√4.9)² = 4.9.
Therefore, the area of the square box is 4.9 square units.
Problem 2
A square-shaped building measuring 4.9 square feet is built; if each of the sides is √4.9, what will be the square feet of half of the building?
2.45 square feet.
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 4.9 by 2 = 2.45.
So half of the building measures 2.45 square feet.
Problem 3
Calculate √4.9 x 5.
11.06795
Explanation
The first step is to find the square root of 4.9, which is approximately 2.21359.
The second step is to multiply 2.21359 by 5.
So, 2.21359 x 5 = 11.06795.
Problem 4
What will be the square root of (4.9 + 0.1)?
The square root is approximately 2.236.
Explanation
To find the square root, we need to find the sum of (4.9 + 0.1). 4.9 + 0.1 = 5. √5 ≈ 2.236.
Therefore, the square root of (4.9 + 0.1) is approximately ±2.236.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4.9 units and the width ‘w’ is 1 unit.
The perimeter of the rectangle is approximately 6.427 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4.9 + 1) = 2 × (2.213 + 1) = 2 × 3.213 = 6.426 units.
FAQ on Square Root of 4.9
1.What is √4.9 in its simplest form?
2.Mention the factors of 4.9.
3.Calculate the square of 4.9.
4.Is 4.9 a prime number?
5.4.9 is divisible by?
Important Glossaries for the Square Root of 4.9
- Square root: A square root is the inverse of a square. Example: 4² = 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.
- Decimal: A number with a whole number and a fraction in a single number, such as 2.21359.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number into parts and solving step by step.
- Perfect square: A number that is the square of an integer, such as 4 (2²) or 9 (3²).
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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.
