Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root has applications in various fields, such as vehicle design and finance. Here, we will discuss the square root of 5/4.
The square root is the inverse operation of squaring a number. The value 5/4 is not a perfect square. The square root of 5/4 can be expressed in both radical and exponential forms. In radical form, it is expressed as √(5/4), whereas in exponential form, it is expressed as (5/4)^(1/2). The square root of 5/4 is approximately 1.11803, which is an irrational number because it cannot be expressed as a fraction of integers.
The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 5/4, we use methods such as the simplification of fractions, the long-division method, and approximation. Let us now explore these methods:
To find the square root of a fraction, we take the square root of the numerator and the denominator separately.
Step 1: The fraction is 5/4.
Step 2: The square root of 5 is √5 and the square root of 4 is √4 = 2.
Step 3: Therefore, the square root of 5/4 is √5/2.
The long division method is used for finding more precise decimal values of square roots. Here’s how we can find the square root of 5/4 using this method:
Step 1: Convert the fraction 5/4 into a decimal, which is 1.25.
Step 2: Group the numbers from the decimal point. In this case, we start with 1.25.
Step 3: Find a number whose square is less than or equal to the first group (1.25). Here, 1 x 1 = 1 is less than 1.25.
Step 4: Subtract 1 from 1.25 to get 0.25, and bring down two zeros to make it 25.
Step 5: Double the quotient (1) and use it as the new divisor: 2x.
Step 6: Find x such that 2x × x is less than or equal to 25. x is 1, as 21 × 1 = 21.
Step 7: Subtract 21 from 25 to get 4, bring down more zeros, and continue the process to get more decimal places.
The square root of 1.25 is approximately 1.11803.
The approximation method provides a quick way to estimate square roots. Here’s how to find the square root of 5/4 using this method:
Step 1: Identify the perfect squares near 1.25. The perfect squares closest to 1.25 are 1 (1^2) and 1.44 (1.2^2).
Step 2: Since 1.25 is closer to 1.44, start with 1.1 as a rough estimate.
Step 3: Calculate 1.1 × 1.1 = 1.21, which is less than 1.25. Step 4: Increase the estimate slightly to find a closer approximation, resulting in approximately 1.11803.
Students make common mistakes when finding square roots, such as forgetting about negative square roots and misapplying methods. Let’s explore these mistakes in detail.
Can you help Max find the area of a square with side length √(5/4)?
The area of the square is approximately 1.25 square units.
Area of the square = side^2.
The side length is given as √(5/4).
Area of the square = (√(5/4))^2 = 5/4 = 1.25.
Therefore, the area of the square is approximately 1.25 square units.
A rectangle has a length of 5 units and a width of √(5/4) units. What is its area?
The area of the rectangle is approximately 5.59015 square units.
Area = length × width = 5 × √(5/4).
First, calculate √(5/4) ≈ 1.11803.
Then, area = 5 × 1.11803 = 5.59015 square units.
Calculate √(5/4) × 8.
Approximately 8.94424.
Find the square root of 5/4, which is approximately 1.11803.
Multiply 1.11803 by 8. 1.11803 × 8 ≈ 8.94424.
What will be the square root of (5 + 4)?
The square root is 3.
Find the sum of (5 + 4) = 9. Then, √9 = 3. Therefore, the square root of (5 + 4) is ±3.
Find the perimeter of a rectangle if its length ‘l’ is 5 units and the width ‘w’ is √(5/4) units.
The perimeter of the rectangle is approximately 12.23606 units.
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (5 + √(5/4)) ≈ 2 × (5 + 1.11803) ≈ 2 × 6.11803 ≈ 12.23606 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.
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