Square Root of 16/49
2026-02-28 06:15 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-16/49

302 Learners

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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 16/49.

What is the Square Root of 16/49?

The square root is the inverse of the square of a number. The fraction 16/49 is a perfect square. The square root of 16/49 is expressed in both radical and exponential form. In radical form, it is expressed as √(16/49), whereas in exponential form it is (16/49)^(1/2). √(16/49) = 4/7, 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 16/49

The prime factorization method is used for perfect square numbers. Since 16/49 is a perfect square, we can use the prime factorization method as well as recognizing perfect squares directly. Let's explore the following methods:

  • Prime factorization method
     
  • Recognizing perfect squares

Square Root of 16/49 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 16/49 is broken down into its prime factors.

Step 1: Finding the prime factors of 16 and 49. For 16, the prime factors are 2 x 2 x 2 x 2 = 2^4. For 49, the prime factors are 7 x 7 = 7^2.

Step 2: Now we found out the prime factors. The square root of 16/49 is √(2^4/7^2) = (2^2/7) = 4/7.

Explore Our Programs

Square Root of 16/49 by Recognizing Perfect Squares

Recognizing perfect squares is an easier method for finding the square roots of fractions that are perfect squares. Let us now learn how to find the square root using this method, step by step.

Step 1: Identify the perfect squares in the numerator and the denominator. 16 is a perfect square, as it is 4^2. 49 is a perfect square, as it is 7^2.

Step 2: The square root of 16/49 is simply the square root of the numerator over the square root of the denominator, which is 4/7.

Common Mistakes and How to Avoid Them in the Square Root of 16/49

Students do make mistakes while finding the square root, like forgetting about the negative square root or incorrectly applying the square root to fractions. Now let us look at a few of those mistakes that students tend to make in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(16/49)?

Okay, lets begin

The area of the square is 16/49 square units.

Explanation

The area of the square = side².

The side length is given as √(16/49).

Area of the square = side² = (4/7) × (4/7) = 16/49.

Therefore, the area of the square box is 16/49 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 16/49 square feet is built; if each of the sides is √(16/49), what will be the square feet of half of the building?

Okay, lets begin

8/49 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 16/49 by 2 = 8/49.

So half of the building measures 8/49 square feet.

Well explained 👍

Problem 3

Calculate √(16/49) × 5.

Okay, lets begin

20/7

Explanation

The first step is to find the square root of 16/49, which is 4/7.

The second step is to multiply 4/7 by 5.

So (4/7) × 5 = 20/7.

Well explained 👍

Problem 4

What will be the square root of (16/49 + 1)?

Okay, lets begin

The square root is 8/7.

Explanation

To find the square root, we need to find the sum of (16/49 + 1).

16/49 + 49/49 = 65/49, and then √(65/49) = 8/7.

Therefore, the square root of (16/49 + 1) is 8/7.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(16/49) units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is 76 + 8/7 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(16/49) + 38) = 2 × (4/7 + 38) = 2 × (4/7 + 266/7) = 2 × 270/7 = 540/7 = 76 + 8/7 units.

Well explained 👍

FAQ on Square Root of 16/49

1.What is √(16/49) in its simplest form?

The simplest form of √(16/49) is 4/7, as both 16 and 49 are perfect squares.

2.Mention the factors of 16/49.

Factors of 16/49 are derived from its numerator and denominator. For 16, factors are 1, 2, 4, 8, 16. For 49, factors are 1, 7, 49.

3.Calculate the square of 16/49.

We get the square of 16/49 by multiplying the number by itself: (16/49) × (16/49) = 256/2401.

4.Is 16/49 a prime number?

16/49 is not a prime number, as it is a fraction composed of two non-prime numbers.

5.16/49 is divisible by?

16/49 is a fraction, so it is divisible by its own factors, which are the factors of 16 and 49. Factors include numbers like 1/49, 2/49, 4/49, 8/49, and 16/49 itself.

Important Glossaries for the Square Root of 16/49

  • Square root: A square root is the inverse operation of squaring a number. For example, 4² = 16, and the square root is √16 = 4.
  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A number that is the square of an integer. For example, 16 and 49 are perfect squares.
  • Fraction: A numerical quantity that is not a whole number, represented by two numbers, one above the other and separated by a line, for example, 3/4.
  • Reciprocal: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 4/7 is 7/4.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.