123 LearnersLast updated on May 26th, 2025
Square Root of 5/3
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 various fields including engineering, finance, etc. Here, we will discuss the square root of 5/3.
What is the Square Root of 5/3?
The square root is the inverse of the square of a number. 5/3 is not a perfect square. The square root of 5/3 is expressed in both radical and exponential form. In radical form, it is expressed as √(5/3), whereas in exponential form it is expressed as (5/3)^(1/2). √(5/3) ≈ 1.29099, 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.
Finding the Square Root of 5/3
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect squares. Instead, methods such as the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 5/3 by Long Division Method
The long division method is particularly used for non-perfect squares. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Convert 5/3 to a decimal: 5/3 ≈ 1.6667.
Step 2: Group the digits of 1.6667 in pairs from the decimal point outward, adding zeros if necessary: 1.66 | 67.
Step 3: Find the largest integer n whose square is less than or equal to 1. The integer is 1 (since 1^2 = 1).
Step 4: Subtract 1 from 1 to get the remainder 0. Bring down the next pair of digits 66 to get 066.
Step 5: Double the quotient obtained and use it as the new divisor's base. The divisor becomes 20.
Step 6: Determine the value of the next digit of the quotient (n) such that 20n × n ≤ 66. Here, n = 3, since 203 × 3 = 609.
Step 7: Subtract 609 from 660 to get the remainder 51, and bring down the next pair of zeros to get 5100.
Step 8: Continue these steps to get the decimal expansion of √(5/3).
So, √(5/3) ≈ 1.29099.
Square Root of 5/3 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 5/3 using the approximation method.
Step 1: Estimate a rough range. Since 5/3 ≈ 1.67, check between √1 and √2.
Step 2: Refine the range using closer approximations. √1.5 ≈ 1.2247 and √2 ≈ 1.4142.
Step 3: Use linear interpolation or trial and error between 1.2247 and 1.4142 to narrow down closer to √1.67.
Step 4: Using interpolation, √(5/3) ≈ 1.29.
Common Mistakes and How to Avoid Them in the Square Root of 5/3
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we usually take only the positive square root for practical purposes.
For example: √(5/3) ≈ 1.29, but there's also -1.29.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol correctly is another common mistake. To resolve this, teach children to simplify numbers inside the square root first and then progress.
For example: √(4/9) should be simplified to 2/3, not √4/√9 separately.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to approximate the value correctly.
For example: √(5/3) ≈ 1.29, not simply 1.
Mistake 4
Confusing the square root symbol with the cube root
Students need to learn the difference between cube root and square root to avoid confusion.
For example: √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, and students might accidentally skip a step, leading to incorrect answers. This could happen during subtraction or elsewhere.
Square Root of 5/3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(5/3)?
The area of the square is approximately 1.667 square units.
Explanation
The area of the square = side^2.
The side length is given as √(5/3).
Area of the square = side^2 = √(5/3) × √(5/3) = 5/3 ≈ 1.667.
Therefore, the area of the square box is approximately 1.667 square units.
Problem 2
A square-shaped garden measuring 5/3 square meters is created; if each side is √(5/3), what will be the area of half of the garden?
Approximately 0.8335 square meters.
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 5/3 by 2 gives us approximately 0.8335.
So, half of the garden measures approximately 0.8335 square meters.
Problem 3
Calculate √(5/3) × 4.
Approximately 5.164.
Explanation
The first step is to find the square root of 5/3, which is approximately 1.29.
The second step is to multiply 1.29 by 4. 1.29 × 4 = 5.164.
Problem 4
What will be the square root of (9 + 1/3)?
The square root is approximately 3.055.
Explanation
To find the square root, we need to find the sum of (9 + 1/3). 9 + 1/3 = 28/3, and then √(28/3) ≈ 3.055.
Therefore, the square root of (9 + 1/3) is approximately ±3.055.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √(5/3) units and the width 'w' is 3 units.
We find the perimeter of the rectangle as approximately 8.58 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(5/3) + 3).
Perimeter ≈ 2 × (1.29 + 3) = 2 × 4.29 ≈ 8.58 units.
FAQ on Square Root of 5/3
1.What is √(5/3) in its simplest form?
2.Mention the factors of 5/3.
3.Calculate the square of 5/3.
4.Is 5/3 a prime number?
5.5/3 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 5/3?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 5/3?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 5/3
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers. √(5/3) is an example.
- Principal square root: Though a number has both positive and negative square roots, the positive square root is often used for practical purposes. This is known as the principal square root.
- Radical: A radical is a symbol (√) used to denote the square root or nth root of a number. For instance, √(5/3) represents the square root of 5/3.
- Rationalization: The process of eliminating a radical from the denominator of a fraction by multiplying the numerator and the denominator by a suitable value is called rationalization.
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Jaskaran Singh Saluja
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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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