Square Root of 49/64
2026-02-28 06:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-49/64

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Last updated on August 5, 2025

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

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(49/64)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(49/64) x 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (49/64 + 15/64)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(49/64) units and the width ‘w’ is 5 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 49/64

1.What is √(49/64) in its simplest form?

The prime factorization of 49 is 7 x 7 and 64 is 2 x 2 x 2 x 2 x 2 x 2, so the simplest form of √(49/64) is 7/8.

2.Mention the factors of 49/64.

Factors of 49/64 are 1/64, 7/64, 1, 1/8, 7/8, and 49/64.

3.Calculate the square of 49/64.

We get the square of 49/64 by multiplying the number by itself, that is (49/64) x (49/64) = 2401/4096.

4.Is 49/64 a prime fraction?

5.49/64 is divisible by?

49/64 is divisible by 1/64, 7/64, 1, 1/8, 7/8, and 49/64.

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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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.