129 LearnersLast updated on May 26th, 2025
Square Root of 49/64
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 like vehicle design, finance, etc. Here, we will discuss the square root of 49/64.
What is the Square Root of 49/64?
The square root is the inverse of the square of the number. 49/64 is a perfect square fraction. The square root of 49/64 is expressed in both radical and exponential form. In radical form, it is expressed as √(49/64), whereas (49/64)^(1/2) in exponential form. √(49/64) = 7/8, 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 49/64
The prime factorization method works well for perfect square numbers, including fractions. Let's discuss the methods commonly used to find square roots:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 49/64 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 49/64 is broken down into its prime factors.
Step 1: Finding the prime factors of 49 and 64 49 can be factored as 7 x 7 64 can be factored as 2 x 2 x 2 x 2 x 2 x 2
Step 2: Since 49 and 64 are both perfect squares, the square root can be directly obtained by taking the square root of the numerator and the denominator separately. √(49/64) = √49 / √64 = 7/8
Square Root of 49/64 by Long Division Method
The long division method is useful for non-perfect square numbers but can also verify perfect squares. Here is how to find the square root using the long division method, step by step:
Step 1: Write the number 49/64 in decimal form, which is 0.765625.
Step 2: Start by grouping digits in pairs from right to left in the decimal.
Step 3: Find the largest integer whose square is less than or equal to the first group. Here, the first group is 0.76, and 0.8 works because 0.8 x 0.8 = 0.64.
Step 4: Subtract, bring down the next group, and repeat the process for each pair.
Step 5: Continue the process until you reach an accurate value. For 0.765625, the square root is exactly 0.875, which confirms our previous result.
Square Root of 49/64 by Approximation Method
Approximation method is another method for finding square roots and is useful for non-perfect squares. However, for fractions like 49/64, we can directly find an exact result:
Step 1: Identify closest perfect squares for the numerator and the denominator.
Step 2: Since 49 and 64 are perfect squares, this method confirms that √49 = 7 and √64 = 8. Thus, √(49/64) = 7/8, which is an exact result.
Common Mistakes and How to Avoid Them in the Square Root of 49/64
Students do make mistakes while finding the square root, such as forgetting about the negative square root or misapplying methods. Let us look at a few of those 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 take only the positive square root for practical purposes.
For example, √(49/64) = 7/8, but there is also -7/8, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake. Ensure simplification of numbers inside the square root before moving on.
For example, √(16/4) = √16 / √4 = 4/2 = 2, not √16/4 = √4.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify numbers inside the square root. This prevents mistakes in approximating values.
For example, √(50/81) ≈ 0.785, not 0.7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to learn the difference between cube root and square root.
For example, √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Many students might skip a step, resulting in a wrong answer. This may occur during subtraction or elsewhere.
Square Root of 49/64 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(49/64)?
The area of the square is 49/64 square units.
Explanation
The area of the square = side².
The side length is given as √(49/64).
Area of the square = (√(49/64))² = 49/64.
Problem 2
A square-shaped building measuring 1 square foot is built; if each of the sides is √(49/64), what will be the square feet of half of the building?
0.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1 by 2 = 0.5.
So half of the building measures 0.5 square feet.
Problem 3
Calculate √(49/64) x 5.
4.375
Explanation
The first step is to find the square root of 49/64, which is 7/8.
The second step is to multiply 7/8 with 5.
So 7/8 x 5 = 4.375.
Problem 4
What will be the square root of (49/64 + 15/64)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (49/64 + 15/64). 49/64 + 15/64 = 64/64 = 1, and then √1 = 1.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(49/64) units and the width ‘w’ is 5 units.
We find the perimeter of the rectangle as 10.75 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (7/8 + 5) = 2 × (0.875 + 5) = 2 × 5.875 = 11.75 units.
FAQ on Square Root of 49/64
1.What is √(49/64) in its simplest form?
2.Mention the factors of 49/64.
3.Calculate the square of 49/64.
4.Is 49/64 a prime fraction?
5.49/64 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 49/64?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 49/64?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 49/64
- 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.
- 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 a positive square root that is more prominent due to its uses in the real world. That is why it is also known as a principal square root.
- Fraction: A fraction represents a part of a whole, expressed as a numerator divided by a denominator. For example, 7/8 is a fraction.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 49 and 64 are perfect squares because they are 7² and 8², respectively.
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About BrightChamps in Oman
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.
