Square Root of 1/49
2026-02-28 06:07 Diff
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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/49.

What is the Square Root of 1/49?

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

Since 1/49 is a perfect square, the prime factorization method is straightforward here. However, it can also be verified using the long division method or the approximation method. Let us explore these methods:

  • Prime factorization method
     
  • Long division method
     
  • Approximation method

Square Root of 1/49 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Now let us look at how 1/49 is broken down into its prime factors.

Step 1: Finding the prime factors of 49 49 = 7 x 7: 7²

Step 2: Since 1 is a perfect square, its square root is 1. Thus, √(1/49) = 1/7.

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Square Root of 1/49 by Long Division Method

The long division method can be used to find the square root of perfect squares as well. Let us now learn how to find the square root using the long division method, step by step:

Step 1: Consider the number 1/49 as 0.0204.

Step 2: Pair the digits from right to left, starting with the decimal point: 02 and 04.

Step 3: The square root of 1 is 1, so our first divisor is 1.

Step 4: Bring down 04, making the new dividend 04.

Step 5: Double the divisor (1), resulting in 2.

Step 6: Find n such that 2n x n ≤ 4. Here, n is 0 because 20 x 0 = 0, and the remainder is 4.

Step 7: Continue with the process for further decimal places, but since this is a perfect square, we find that √(1/49) = 0.142857... which simplifies to 1/7.

Square Root of 1/49 by Approximation Method

The approximation method involves identifying the perfect squares close to our number and estimating based on those.

Step 1: Identify the perfect squares around 1/49, which are 0 and 1.

Step 2: The square root of 0 is 0, and the square root of 1 is 1, so √(1/49) falls between these values.

Step 3: Since 1/49 is exactly 1/7, the approximation method confirms the exact value: √(1/49) = 1/7.

Common Mistakes and How to Avoid Them in the Square Root of 1/49

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping calculation steps. Let's discuss some common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/64)?

Okay, lets begin

The area of the square is 1/64 square units.

Explanation

The area of the square = side².

The side length is given as √(1/64).

Area of the square = side² = √(1/64) x √(1/64) = 1/8 x 1/8 = 1/64.

Therefore, the area of the square box is 1/64 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 1/49 square units is built; if each of the sides is √(1/49), what will be the square units of half of the garden?

Okay, lets begin

1/98 square units

Explanation

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

Dividing (1/49) by 2 = 1/98.

So half of the garden measures 1/98 square units.

Well explained 👍

Problem 3

Calculate √(1/49) x 5.

Okay, lets begin

5/7

Explanation

The first step is to find the square root of 1/49, which is 1/7.

The second step is to multiply 1/7 with 5.

So 1/7 x 5 = 5/7.

Well explained 👍

Problem 4

What will be the square root of (1/64 + 1/64)?

Okay, lets begin

The square root is 1/8.

Explanation

To find the square root, we need to find the sum of (1/64 + 1/64). 1/64 + 1/64 = 1/32, and then √(1/32) = 1/√32 = 1/8.

Therefore, the square root of (1/64 + 1/64) is 1/8.

Well explained 👍

Problem 5

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

Okay, lets begin

We find the perimeter of the rectangle as 2.2857 units.

Explanation

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

Perimeter = 2 × (√(1/49) + 1) = 2 × (1/7 + 1) = 2 × (1.142857) = 2.2857 units.

Well explained 👍

FAQ on Square Root of 1/49

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

√(1/49) simplifies to 1/7, as 49 is a perfect square, and 1 is also a perfect square.

2.Mention the factors of 49.

Factors of 49 are 1, 7, and 49.

3.Calculate the square of 1/49.

We get the square of 1/49 by multiplying the number by itself, that is (1/49) x (1/49) = 1/2401.

4.Is 49 a prime number?

49 is not a prime number, as it has more than two factors: 1, 7, and 49.

5.49 is divisible by?

49 is divisible by 1, 7, and 49.

Important Glossaries for the Square Root of 1/49

  • Square root: A square root is the inverse of a square. Example: 7² = 49, and the inverse of the square is the square root, so √49 = 7.
  • 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.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 49 is a perfect square because it is 7².
  • Prime number: A prime number is a number greater than 1 with no divisors other than 1 and itself.
  • Decimal: If a number has a whole number and a fractional part, it is called a decimal. For example: 0.142857 is a decimal.

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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.