104 LearnersLast updated on May 26th, 2025
Square Root of 3.24
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 3.24.
What is the Square Root of 3.24?
The square root is the inverse of the square of the number. 3.24 is a perfect square. The square root of 3.24 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.24, whereas (3.24)^(1/2) in the exponential form. √3.24 = 1.8, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 3.24
The prime factorization method can be used for perfect square numbers. Let's learn the methods used for finding square roots:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3.24 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. For 3.24, we first convert it to a fraction to find its prime factors.
Step 1: Convert 3.24 to a fraction, which is 324/100.
Step 2: Find the prime factors of 324, which are 2 x 2 x 3 x 3 x 3 x 3 (or 2^2 x 3^4).
Step 3: Pair the prime factors: (2 x 2) and (3 x 3) x (3 x 3).
Step 4: Take the square root of each pair: √(2^2) = 2, √(3^4) = 3 x 3 = 9.
Step 5: The square root of 324 is 18.
Since 324 was divided by 100, we also divide 18 by 10, resulting in 1.8.
Square Root of 3.24 by Long Division Method
The long division method is particularly useful for non-perfect square numbers but can be applied to perfect squares too. Here’s how to find the square root using the long division method:
Step 1: Group the numbers from right to left. For 3.24, we treat it like 324.
Step 2: Find the largest number whose square is less than or equal to 3. The number is 1. The quotient is 1, and the remainder is 2.
Step 3: Bring down the next pair of digits (24), making it 224.
Step 4: Double the current quotient (1), which gives us 2. This becomes our new divisor.
Step 5: Find a number (n) such that 2n x n ≤ 224. Here, n = 8 works, as 28 x 8 = 224.
Step 6: Subtract 224 from 224 to get a remainder of 0.
Step 7: Since there is no remainder, the square root of 3.24 is exactly 1.8.
Square Root of 3.24 by Approximation Method
The approximation method provides an easy way to find square roots, suitable for both perfect and non-perfect squares.
Step 1: Identify the closest perfect squares around 3.24, which are 1 (with square root 1) and 4 (with square root 2).
Step 2: Since 3.24 is closer to 4, estimate the square root to be closer to 2.
Step 3: Use a calculator or further approximation steps to find that the square root of 3.24 is exactly 1.8.
Common Mistakes and How to Avoid Them in the Square Root of 3.24
Students make mistakes while finding the square root, like forgetting about the negative square root or misapplying methods. Here are some common mistakes:
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 take only the positive square root in practical scenarios.
For example: √3.24 = 1.8, but there is also -1.8, which should not be ignored.
Square Root of 3.24 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3.24?
The area of the square is 3.24 square units.
Explanation
The area of the square = side^2.
The side length is given as √3.24.
Area of the square = side^2 = √3.24 x √3.24 = 1.8 x 1.8 = 3.24.
Therefore, the area of the square box is 3.24 square units.
Problem 2
A square-shaped building measuring 3.24 square meters is built; if each side is √3.24, what will be the square meters of half of the building?
1.62 square meters.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3.24 by 2 gives 1.62.
So half of the building measures 1.62 square meters.
Problem 3
Calculate √3.24 x 5.
9
Explanation
The first step is to find the square root of 3.24, which is 1.8.
The second step is to multiply 1.8 by 5. So 1.8 x 5 = 9.
Problem 4
What will be the square root of (3 + 0.24)?
The square root is 1.8.
Explanation
To find the square root, we need to find the sum of (3 + 0.24). 3 + 0.24 = 3.24, and then √3.24 = 1.8.
Therefore, the square root of (3 + 0.24) is ±1.8.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3.24 units and the width ‘w’ is 2 units.
The perimeter of the rectangle is 7.6 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√3.24 + 2) = 2 × (1.8 + 2) = 2 × 3.8 = 7.6 units.
FAQ on Square Root of 3.24
1.What is √3.24 in its simplest form?
2.Mention the factors of 3.24.
3.Calculate the square of 3.24.
4.Is 3.24 a prime number?
5.What is the decimal form of the square root of 3.24?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 3.24?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 3.24?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 3.24
- Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse is the square root, √16 = 4.
- Rational number: A rational number can be expressed as a fraction p/q, where q is not zero and p and q are integers.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square as it is 4^2.
- Decimal: A decimal is a number that includes a whole number and fractional part separated by a decimal point. For example, 7.86.
- Long division method: A technique used to find the square root of numbers, especially useful for both perfect and non-perfect squares.
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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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