120 LearnersLast updated on May 26th, 2025
Square Root of 49/9
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 and finance. Here, we will discuss the square root of 49/9.
What is the Square Root of 49/9?
The square root is the inverse of the square of the number. 49/9 is a perfect square fraction. The square root of 49/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(49/9), whereas in exponential form it is expressed as (49/9)^(1/2). √(49/9) = 7/3, 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 49/9
For perfect square numbers, the prime factorization method can be used. However, since 49/9 is a simple fraction of perfect squares, we can directly find its square root. Let us now learn the following methods:
- Direct method for perfect square fractions
- Verification by multiplication
Square Root of 49/9 by Direct Method
Since 49 and 9 are both perfect squares, we can find the square root of each separately.
Step 1: Find the square root of the numerator (49). √49 = 7
Step 2: Find the square root of the denominator (9). √9 = 3 Therefore, √(49/9) = 7/3.
Square Root of 49/9 by Verification
We can verify our result by squaring the outcome of the square root to check if it equals the original number.
Step 1: Square the result obtained from the direct method. (7/3)² = 49/9
Step 2: Compare it with the original fraction. Since (7/3)² equals 49/9, our result is verified.
Common Mistakes and How to Avoid Them in the Square Root of 49/9
Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us look at a few common mistakes in detail.
Common Mistakes and How to Avoid Them in the Square Root of 49/9
Students often make mistakes while finding the square root, such as confusing the process for non-perfect square numbers or forgetting about negative square roots. Let us look at a few 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 usually consider only the positive square root in practical scenarios.
For example, √(49/9) = 7/3, but there is also -7/3.
Mistake 2
Not simplifying square roots of fractions correctly
Students may incorrectly simplify the square root of a fraction by not taking square roots of both the numerator and the denominator separately.
For example, √(49/9) = 7/3, not 7/9.
Mistake 3
Confusing perfect square fractions with non-perfect square fractions
Ensure students understand the difference between perfect and non-perfect square fractions, as this affects whether direct methods or approximation methods are needed. √(49/9) is straightforward because it is a perfect square fraction.
Mistake 4
Errors in arithmetic operations
Ensure students correctly perform arithmetic operations when verifying or calculating square roots.
For example, squaring 7/3 should yield 49/9.
Mistake 5
Misinterpretation of square root symbols
Students may confuse square root symbols with cube roots or other operations. Emphasize the correct interpretation of √ as the square root.
Square Root of 49/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(49/9)?
The area of the square is 49/9 square units.
Explanation
The area of the square = side².
The side length is given as √(49/9).
Area of the square = (7/3) × (7/3) = 49/9.
Therefore, the area of the square box is 49/9 square units.
Problem 2
A square-shaped building measuring 49/9 square feet is built; if each of the sides is √(49/9), what will be the square feet of half of the building?
24.5/9 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 49/9 by 2 = 24.5/9.
So half of the building measures 24.5/9 square feet.
Problem 3
Calculate √(49/9) × 5.
35/3
Explanation
The first step is to find the square root of 49/9, which is 7/3.
The second step is to multiply 7/3 by 5.
So (7/3) × 5 = 35/3.
Problem 4
What will be the square root of (49/9 + 1)?
The square root is 4/3.
Explanation
To find the square root, we need to find the sum of (49/9 + 1). 49/9 + 9/9 = 58/9. √(58/9) is not an integer, but if simplified, it falls between 2 and 3.
Since 58 is close to 64, which is a perfect square, we can approximate it as √64/9 = 8/3.
Therefore, the square root of (49/9 + 1) is approximately 4/3.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(49/9) units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 84/3 + 76 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (7/3 + 38) = 2 × (84/3 + 114/3) = 2 × 198/3 = 396/3 = 132 units.
FAQ on Square Root of 49/9
1.What is √(49/9) in its simplest form?
2.Mention the factors of 49/9.
3.Calculate the square of 49/9.
4.Is 49/9 a rational number?
5.49/9 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 49/9?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 49/9?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 49/9
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, which 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.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because 7² = 49.
- Fraction: A fraction is a way to represent a part of a whole, expressed as a ratio of two integers, such as 1/2 or 49/9.
- Approximation: An approximation is a value or number that is close to but not exactly equal to the actual value, often used when exact values are difficult to obtain.
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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.
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