Square Root of 4/49
2026-02-28 12:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4-by-49

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Last updated on December 15, 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 4/49.

What is the Square Root of 4/49?

The square root is the inverse of the square of a number. 4/49 is a perfect square.

The square root of 4/49 can be expressed in both radical and exponential form.

In radical form, it is expressed as √(4/49), whereas in exponential form it is expressed as (4/49)^(1/2).

√(4/49) = 2/7, 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 4/49

Finding the square root of a fraction involves taking the square root of the numerator and the denominator separately.

Since 4 and 49 are both perfect squares, we can use the simple method of finding their individual square roots:

Step 1: Find the square root of the numerator, which is √4 = 2.

Step 2: Find the square root of the denominator, which is √49 = 7.

Step 3: Write the square root of 4/49 as the fraction of the square roots of the numerator and denominator, which is 2/7.

Square Root of 4/49 by Prime Factorization Method

The prime factorization method is used to find the square roots of numbers by breaking them into their prime factors.

Step 1: Finding the prime factors of 4 and 49. Breaking down 4, we get 2 x 2: 2^2. Breaking down 49, we get 7 x 7: 7^2.

Step 2: Since both numbers are perfect squares, we can find the square root by taking one of each pair of prime factors: √(4/49) = √(2^2 / 7^2) = 2/7.

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Square Root of 4/49 by Long Division Method

Since 4/49 is a perfect square fraction, the long division method is not necessary.

However, in general, for non-perfect square fractions, the long division method can be used to approximate the square root.

Here, we can directly use the simplest form derived from the prime factorization method, which is 2/7.

Square Root of 4/49 by Approximation Method

For fractions like 4/49 that are perfect squares, approximation is not needed as the exact square root can be determined.

However, the approximation method involves identifying the nearest perfect squares and estimating between them.

Given √(4/49) = 2/7, no approximation is necessary as it is a precise value.

Common Mistakes and How to Avoid Them in the Square Root of 4/49

Students can make common mistakes while finding square roots, such as forgetting to simplify the fraction or incorrectly identifying the square root of the numerator or denominator.

Let's review some common mistakes and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(4/49)?

Okay, lets begin

The area of the square is 4/49 square units.

Explanation

The area of the square = side^2.

The side length is given as √(4/49).

Area of the square = side^2 = (2/7) x (2/7) = 4/49.

Therefore, the area of the square box is 4/49 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4/49 square feet is built; if each of the sides is √(4/49), what will be the square feet of half of the building?

Okay, lets begin

2/49 square feet

Explanation

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

Dividing 4/49 by 2 = we get 2/49.

So half of the building measures 2/49 square feet.

Well explained 👍

Problem 3

Calculate √(4/49) x 5.

Okay, lets begin

10/7

Explanation

The first step is to find the square root of 4/49, which is 2/7.

The second step is to multiply 2/7 by 5.

So (2/7) x 5 = 10/7.

Well explained 👍

Problem 4

What will be the square root of (4/49 + 5/49)?

Okay, lets begin

The square root is 1.

Explanation

To find the square root, we first find the sum of (4/49 + 5/49).

(4/49) + (5/49) = 9/49, and then √(9/49) = 3/7.

Therefore, the square root of (4/49 + 5/49) is 1/7.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(4/49) units and the width ‘w’ is 1 unit.

Okay, lets begin

The perimeter of the rectangle is 16/7 units.

Explanation

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

Perimeter = 2 × (√(4/49) + 1)

= 2 × (2/7 + 1)

= 2 × (9/7)

= 18/7 units.

Well explained 👍

FAQ on Square Root of 4/49

1.What is √(4/49) in its simplest form?

The square root of 4/49 is already in its simplest form, which is 2/7.

2.Mention the factors of 4 and 49.

Factors of 4 are 1, 2, and 4.

Factors of 49 are 1, 7, and 49.

3.Calculate the square of 4/49.

We get the square of 4/49 by multiplying the number by itself, that is (4/49) x (4/49) = 16/2401.

4.Is 4/49 a perfect square?

Yes, 4/49 is a perfect square, as its square root is 2/7, which is a rational number.

5.What is the decimal representation of √(4/49)?

Important Glossaries for the Square Root of 4/49

  • Square root: A square root is the inverse of a square. Example: 3^2 = 9, and the inverse of the square is the square root that is √9 = 3.
  • 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.
  • Fraction: A fraction is a way to represent a part of a whole by using two numbers, the numerator and the denominator.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because it is 7^2.
  • Simplified form: The simplest form of a fraction is when the numerator and denominator have no common factors other than 1.

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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.