Last updated on May 26th, 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.
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.
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:
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.
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.
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.
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.
Can you help Max find the area of a square box if its side length is given as √(1/64)?
The area of the square is 1/64 square units.
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.
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?
1/98 square units
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.
Calculate √(1/49) x 5.
5/7
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.
What will be the square root of (1/64 + 1/64)?
The square root is 1/8.
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.
Find the perimeter of the rectangle if its length 'l' is √(1/49) units and the width 'w' is 1 unit.
We find the perimeter of the rectangle as 2.2857 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/49) + 1) = 2 × (1/7 + 1) = 2 × (1.142857) = 2.2857 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.