102 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.
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.
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: He loves to play the quiz with kids through algebra to make kids love it.
