122 LearnersLast updated on May 26th, 2025
Square Root of 5/4
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.
What is 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.
Finding the Square Root of 5/4
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:
- Simplification of fractions
- Long division method
- Approximation method
Square Root of 5/4 by Simplification of Fractions
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.
Square Root of 5/4 by Long Division Method
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.
Square Root of 5/4 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 5/4
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.
Mistake 1
Forgetting about the negative square root
It is crucial to remind students that numbers have both positive and negative square roots. However, we usually focus on the positive square root, as it is more commonly used.
For example, √(5/4) ≈ 1.11803, but there is also -1.11803.
Mistake 2
Not adding square root symbols in proper places
Improper use of square root symbols is a common issue. To avoid this, ensure students simplify expressions inside the square root before further calculations.
For example, √(9+16) ≠ √9 + √16. The correct approach is √(9+16) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
Students often incorrectly approximate non-perfect squares. Teach them to simplify expressions first for accurate approximations.
For example, √(5/4) ≈ 1.11803, not 1.
Mistake 4
Confusing the square root symbol with the cube root
Differentiate between square roots and cube roots regularly to prevent confusion.
For example, √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
The long division method involves many steps, and students might skip steps accidentally, leading to errors. Practice each step carefully, especially subtraction and bringing down new digits.
Square Root of 5/4 Examples
Problem 1
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.
Explanation
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.
Problem 2
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.
Explanation
Area = length × width = 5 × √(5/4).
First, calculate √(5/4) ≈ 1.11803.
Then, area = 5 × 1.11803 = 5.59015 square units.
Problem 3
Calculate √(5/4) × 8.
Approximately 8.94424.
Explanation
Find the square root of 5/4, which is approximately 1.11803.
Multiply 1.11803 by 8. 1.11803 × 8 ≈ 8.94424.
Problem 4
What will be the square root of (5 + 4)?
The square root is 3.
Explanation
Find the sum of (5 + 4) = 9. Then, √9 = 3. Therefore, the square root of (5 + 4) is ±3.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (5 + √(5/4)) ≈ 2 × (5 + 1.11803) ≈ 2 × 6.11803 ≈ 12.23606 units.
FAQ on Square Root of 5/4
1.What is √(5/4) in its simplest form?
2.Mention the factors of 5/4.
3.Calculate the square of 5/4.
4.Is 5/4 a rational number?
5.What is the decimal representation of 5/4?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 5/4?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 5/4?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 5/4
- Square root: The square root is the operation that finds a number which, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, as 2 × 2 = 4.
- Rational number: A rational number can be expressed as a fraction of two integers, where the denominator is not zero.
- Irrational number: An irrational number cannot be expressed as a simple fraction of two integers. Example: The square root of 2 is irrational.
- Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.
- Decimal: A decimal is a number that has a whole number and a fractional part separated by a decimal point. Example: 1.25 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.
