Last updated on May 26th, 2025
If a number is multiplied by itself, 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 5/2.
The square root is the inverse of the square of a number. 5/2 is not a perfect square. The square root of 5/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(5/2), whereas (5/2)^(1/2) in the exponential form. √(5/2) ≈ 1.58114, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 5/2, the long-division method and approximation method are used. Let us now learn the following methods:
The prime factorization method is generally used for integers. Since 5/2 is a fraction, prime factorization is not directly applicable. However, we can separately factor the numerator and denominator if needed.
Step 1: Factor the numerator and the denominator. 5 is a prime number, and 2 is also a prime number.
Step 2: Since 5/2 is not a perfect square, calculating its square root using prime factorization alone is not feasible.
The long division method is particularly used for non-perfect square numbers. Let's apply the long division method to find the square root of 5/2.
Step 1: Convert the fraction 5/2 to a decimal, which is 2.5.
Step 2: Use the long division method to find the square root of 2.5.
Step 3: Group the numbers from right to left. For 2.5, we consider 25 (in the context of the long division method).
Step 4: Find n whose square is less than or equal to 2.5. Here, n is 1, as 1 × 1 = 1.
Step 5: Subtract 1 from 2.5 to get 1.5, then bring down two zeroes to make it 150.
Step 6: Double the quotient (1) to get 2 as the new divisor, and find the largest n such that 2n × n is less than or equal to 150. Here, n is 5, as 25 × 5 = 125.
Step 7: Continue the process to find more decimal places if needed.
So the square root of 5/2 ≈ 1.58114.
The approximation method is another method for finding the square roots and is an easy way to find the square root of a given number. Let's learn how to find the square root of 5/2 using this method.
Step 1: Convert 5/2 to a decimal, which is 2.5.
Step 2: Find the closest perfect squares around 2.5. The smallest perfect square is 1, and the largest is 4.
Step 3: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) For 2.5, (2.5 - 1) / (4 - 1) = 0.5.
Step 4: Using the formula, we add 1 (the integer part of the square root of the smallest perfect square) to get approximately 1.58114.
So the square root of 5/2 is approximately 1.58114.
Students often make mistakes while finding square roots, such as forgetting about the negative square root or misapplying methods. Let's explore a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(5/2)?
The area of the square is approximately 3.75 square units.
The area of the square = side^2.
The side length is given as √(5/2).
Area = (√(5/2))^2 = 5/2 = 2.5 square units.
Therefore, the area of the square box is 2.5 square units.
A square-shaped building measuring 5/2 square feet is built. If each of the sides is √(5/2), what will be the square feet of half of the building?
1.25 square feet
Divide the given area by 2 as the building is square-shaped.
Dividing 5/2 by 2, we get 5/4 = 1.25 So half of the building measures 1.25 square feet.
Calculate √(5/2) × 5.
Approximately 7.9057
First, find the square root of 5/2 which is approximately 1.58114, then multiply it by 5.
So, 1.58114 × 5 ≈ 7.9057
What will be the square root of (5/2 + 1)?
The square root is approximately 1.87083
To find the square root, first calculate the sum of (5/2 + 1). 5/2 + 1 = 7/2 = 3.5
Then, √3.5 ≈ 1.87083.
Therefore, the square root of (5/2 + 1) is approximately ±1.87083
Find the perimeter of the rectangle if its length ‘l’ is √(5/2) units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 9.16228 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(5/2) + 3)
Perimeter ≈ 2 × (1.58114 + 3) = 2 × 4.58114 ≈ 9.16228 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.