106 LearnersLast updated on May 26th, 2025
Square Root of 0.49
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 0.49.
What is the Square Root of 0.49?
The square root is the inverse of the square of the number. 0.49 is a perfect square. The square root of 0.49 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.49, whereas (0.49)^(1/2) in exponential form. √0.49 = 0.7, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 0.49
The prime factorization method is used for perfect square numbers. Since 0.49 is a perfect square, the prime factorization method can be used here. Let us now learn the following methods: -
- Prime factorization method
- Long division method
- Approximation method
Square Root of 0.49 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 0.49 is broken down into its prime factors.
Step 1: Express 0.49 as a fraction, 49/100.
Step 2: Find the prime factors of 49 and 100. 49 = 7 x 7 100 = 10 x 10
Step 3: Take the square root of each factor. √49 = 7 √100 = 10
Step 4: The square root of 0.49 is 7/10 = 0.7.
Square Root of 0.49 by Long Division Method
The long division method is a systematic way to find the square root of any number, especially useful for non-perfect squares, but we can use it here for practice.
Step 1: Consider 0.49 as 49/100.
Step 2: Find a number whose square is less than or equal to 49. The number is 7, as 7 x 7 = 49.
Step 3: Now, since 49 is exactly 7 squared, there is no remainder.
Step 4: As both the numerator and denominator are perfect squares, the square root is 0.7 (as already calculated).
Square Root of 0.49 by Approximation Method
The approximation method is another method for finding square roots, which is helpful if you don't know the exact square roots.
Step 1: Identify the perfect squares between which 0.49 lies. 0.16 (√0.16 = 0.4) and 1.00 (√1.00 = 1.0) 0.49 is closer to 0.4 and 0.7.
Step 2: Calculate a rough approximation by taking midpoints, but since 0.49 is a perfect square, we already know the square root is exactly 0.7.
Common Mistakes and How to Avoid Them in the Square Root of 0.49
Students do make mistakes while finding the square root, like forgetting about the negative square root or misplacing decimal points. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √0.49 = 0.7, there is also -0.7 which should not be forgotten.
Square Root of 0.49 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.81?
The area of the square is 0.81 square units.
Explanation
The area of the square = side².
The side length is given as √0.81.
Area of the square = side²
= (√0.81) x (√0.81)
= 0.9 x 0.9
= 0.81.
Therefore, the area of the square box is 0.81 square units.
Problem 2
A square-shaped building measuring 0.49 square feet is built; if each of the sides is √0.49, what will be the square feet of half of the building?
0.245 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 0.49 by 2 = we get 0.245.
So half of the building measures 0.245 square feet.
Problem 3
Calculate √0.49 x 5.
3.5
Explanation
The first step is to find the square root of 0.49, which is 0.7.
The second step is to multiply 0.7 with 5. So 0.7 x 5 = 3.5.
Problem 4
What will be the square root of (0.36 + 0.13)?
The square root is 0.7.
Explanation
To find the square root, we need to find the sum of (0.36 + 0.13).
0.36 + 0.13 = 0.49, and then √0.49 = 0.7.
Therefore, the square root of (0.36 + 0.13) is ±0.7.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √0.64 units and the width ‘w’ is 0.5 units.
We find the perimeter of the rectangle as 2.8 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√0.64 + 0.5)
= 2 × (0.8 + 0.5)
= 2 × 1.3
= 2.6 units.
FAQ on Square Root of 0.49
1.What is √0.49 in its simplest form?
2.Is 0.49 a perfect square?
3.Calculate the square of 0.49.
4.Is 0.49 a rational number?
5.How do you express 0.49 as a fraction?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 0.49?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 0.49?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 0.49
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √0.49 = 0.7.
- Perfect square: A perfect square is a number that is the square of an integer or a rational number. Example: 0.49 is a perfect square of 0.7.
- Rational number: A rational number is a number that can be expressed as the quotient or fraction of two integers. Example: 0.49 is rational because it can be written as 49/100.
- Decimal: A decimal is a number that has a whole number and a fractional part separated by a decimal point. Example: 0.7, 0.49.
- Long division method: A method of dividing numbers to find the square root, especially useful for determining the square root of non-perfect squares.
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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
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