126 LearnersLast updated on May 26th, 2025
Square Root of 16/3
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 fields such as engineering, mathematics, and physics. Here, we will discuss the square root of 16/3.
What is the Square Root of 16/3?
The square root is the inverse of the square of a number. 16/3 is not a perfect square. The square root of 16/3 is expressed in both radical and exponential form. In radical form, it is expressed as √(16/3), whereas (16/3)^(1/2) is the exponential form. √(16/3) = 2.3094, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 16/3
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, we use methods like long division and approximation. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 16/3 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Here is how to find the square root of 16/3 using the long division method:
Step 1: Convert the fraction 16/3 into a decimal. 16/3 = 5.3333...
Step 2: Use the long division method to find the square root of 5.3333.
Step 3: Estimate a number whose square is less than or equal to 5. Start with 2 because 2^2 = 4, which is less than 5.3333.
Step 4: Bring down the next pair of digits after the decimal point. Divide 1.3333 by 4 to get 0.3333.
Step 5: Continue the division to get more decimal places. The quotient becomes 2.3094 when rounded to four decimal places.
So, the square root of √(16/3) is approximately 2.3094.
Square Root of 16/3 by Approximation Method
The approximation method is another way to find square roots. It is a simple method to estimate the square root of a given number. Now let us learn how to find the square root of 16/3 using the approximation method.
Step 1: Estimate the value of √(5.3333) since 16/3 = 5.3333.
Step 2: Find two numbers between which 5.3333 lies. It lies between 4 (2^2) and 9 (3^2).
Step 3: Use interpolation to approximate the value. Given number = 5.3333 Smallest perfect square = 4 Largest perfect square = 9 Using the formula: (5.3333 - 4) / (9 - 4) ≈ 0.2667
Step 4: Add the decimal to the smaller root value: 2 + 0.2667 = 2.2667 So, the square root of 16/3 is approximately 2.2667.
Common Mistakes and How to Avoid Them in the Square Root of 16/3
Students often make mistakes while finding the square root, such as ignoring the negative square root or skipping methods like long division. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root.
For example, √25 = 5, but there is also -5.
Mistake 2
Not Adding the Square Root Symbol in Proper Places
Incorrect use of the square root symbol can lead to errors. To resolve this, teach students to simplify the numbers inside the square root first.
For example, √(12+24) = √36, not √12 + √24.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
Students should simplify numbers inside the square root to avoid mistakes in identifying approximate values.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
Students need to understand the difference between the cube root and the square root to avoid confusion.
For example, √50 and ∛50 are different.
Mistake 5
Making Mistakes in Long Division
Finding a square root using the long division method involves multiple steps. Students might skip a step accidentally, resulting in a wrong answer. This error could occur in subtraction or elsewhere.
Square Root of 16/3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(25/3)?
The area of the square is approximately 27.778 square units.
Explanation
The area of the square = side^2.
The side length is given as √(25/3).
Area of the square = (√(25/3))^2 = 25/3 ≈ 8.333
Therefore, the area of the square box is approximately 27.778 square units.
Problem 2
A square-shaped garden measures 16/3 square meters. If each of the sides is √(16/3), what will be the square meters of half of the garden?
8/3 square meters.
Explanation
We divide the given area by 2 since the garden is square-shaped.
Dividing 16/3 by 2 gives us 8/3.
So, half of the garden measures 8/3 square meters.
Problem 3
Calculate √(16/3) × 6.
Approximately 13.8564.
Explanation
First, find the square root of 16/3, which is approximately 2.3094.
Then multiply 2.3094 by 6.
So, 2.3094 × 6 ≈ 13.8564.
Problem 4
What will be the square root of (16/3 + 2/3)?
The square root is approximately 2.
Explanation
First, find the sum of (16/3 + 2/3). 16/3 + 2/3 = 18/3 = 6.
Then, find the square root of 6, which is approximately 2.4495.
Therefore, the square root of (16/3 + 2/3) is approximately ±2.4495.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(16/3) units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 14.6188 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(16/3) + 5)
Perimeter = 2 × (2.3094 + 5) ≈ 14.6188 units.
FAQ on Square Root of 16/3
1.What is √(16/3) in its simplest form?
2.Is 16/3 a perfect square?
3.Calculate the square of 16/3.
4.Is 16/3 a rational number?
5.16/3 is divisible by?
Important Glossaries for the Square Root of 16/3
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse of the square is the square root, √16 = 4.
- Irrational number: An irrational number cannot be expressed as a ratio of two integers. For example, √2, which cannot be written as a simple fraction.
- Radical expression: A radical expression includes a root symbol, such as √x, where x is the radicand.
- Approximation: An approximation is an estimated value that is close to but not exactly equal to the true value.
- Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
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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.
