104 LearnersLast updated on May 26th, 2025
Square Root of 49/81
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 49/81.
What is the Square Root of 49/81?
The square root is the inverse operation of squaring a number. The fraction 49/81 is a perfect square. The square root of 49/81 can be expressed in both radical and exponential form. In radical form, it is written as √(49/81), and in exponential form, it is written as (49/81)^(1/2). The square root of 49/81 is 7/9, 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 49/81
The prime factorization method is used for perfect square numbers, including fractions. Let's explore the methods to find the square root of a fraction:
- Prime factorization method
- Simplification method
Square Root of 49/81 by Prime Factorization Method
The prime factorization method involves expressing numbers as the product of their prime factors. Let's see how 49/81 is broken down:
Step 1: Prime factorization of 49 is 7 × 7, and for 81, it is 3 × 3 × 3 × 3.
Step 2: We can write 49/81 as (7 × 7)/(3 × 3 × 3 × 3).
Step 3: Taking the square root of both the numerator and the denominator separately gives us √49/√81 = 7/9. Therefore, the square root of 49/81 is 7/9.
Square Root of 49/81 by Simplification Method
The simplification method involves simplifying the fraction before finding its square root. Let's see how we can do this:
Step 1: Identify the perfect squares in the numerator and denominator. 49 is a perfect square of 7, and 81 is a perfect square of 9.
Step 2: The square root of 49 is 7, and the square root of 81 is 9.
Step 3: Thus, the square root of 49/81 is 7/9.
Square Root of 49/81 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(49/81)?
The area of the square is 49/81 square units.
Explanation
The area of the square = side².
The side length is given as √(49/81).
Area = (7/9) × (7/9) = 49/81.
Therefore, the area of the square box is 49/81 square units.
Problem 2
A square-shaped plot measures 49/81 square meters in area; if each side is √(49/81), what will be the area of half of the plot?
49/162 square meters
Explanation
The plot's area is 49/81 square meters.
To find half of this area, divide by 2. (49/81) ÷ 2 = 49/162.
So, half of the plot measures 49/162 square meters.
Problem 3
Calculate √(49/81) × 5.
35/9
Explanation
First, find the square root of 49/81, which is 7/9.
Then multiply by 5. (7/9) × 5 = 35/9.
Problem 4
What will be the square root of (49/81 + 1)?
The square root is 4/3.
Explanation
Sum the fraction with 1: (49/81 + 81/81) = 130/81.
Now, find the square root: √(130/81) ≈ 4/3.
Therefore, the square root of (49/81 + 1) is approximately ±4/3.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(49/81) units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 85.56 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (7/9 + 38) = 2 × (0.778 + 38) = 2 × 38.778 = 77.556 units.
FAQ on Square Root of 49/81
1.What is √(49/81) in its simplest form?
2.Mention the factors of 49 and 81.
3.Calculate the square of 49/81.
4.Is 49/81 a perfect square?
5.What are the prime factors of 49 and 81?
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 49/81?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 49/81?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 49/81
- Square root: A square root is the operation that finds a value that, when multiplied by itself, gives the original number. Example: The square root of 16 is 4 because 4 × 4 = 16.
- Rational number: A rational number can be expressed as the ratio of two integers, where the denominator is not zero.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3².
- Fraction: A fraction represents a part of a whole or a division of quantities. It is expressed as a numerator over a denominator, like 3/4.
- Exponent: An exponent refers to the number of times a number is multiplied by itself. In the expression 2³, 3 is the exponent, indicating 2 is used as a factor three times: 2 × 2 × 2.
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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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