Last updated on May 26th, 2025
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9/4.
The square root is the inverse of the square of the number. 9/4 is a perfect square. The square root of 9/4 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(9/4), whereas (9/4)^(1/2) in the exponential form. √(9/4) = 3/2 = 1.5, 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.
The square root of a fraction can be found by taking the square root of the numerator and the denominator separately. Let us now explore the methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 9/4 is broken down into its prime factors.
Step 1: Finding the prime factors of 9 and 4 Breaking it down, 9 = 3 × 3 and 4 = 2 × 2.
Step 2: Now we pair the prime factors. The square root of 9 is 3 (since 3 × 3 = 9) and the square root of 4 is 2 (since 2 × 2 = 4).
Therefore, calculating √(9/4) using prime factorization gives us 3/2.
The long division method is particularly used for non-perfect square numbers, but it can also be applied to fractions. Let us learn how to find the square root using the long division method, step by step.
Step 1: Consider the fraction 9/4. We can find the square root of the numerator and denominator separately.
Step 2: The square root of 9 is 3 and the square root of 4 is 2.
Step 3: Therefore, the square root of 9/4 is 3/2.
Approximation method is another method for finding square roots, especially useful for non-perfect squares, but not needed here as 9/4 is a perfect square. However, let us briefly consider this method.
Step 1: Identify the closest perfect squares to 9 and 4, which are 9 and 4 themselves.
Step 2: Since both the numerator and the denominator are perfect squares, the square root of 9/4 is exactly 3/2 or 1.5 without needing approximation.
Students may make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions. Let's look at a few common errors in detail.
Can you help Max find the area of a square box if its side length is given as √(9/4)?
The area of the square is 2.25 square units.
The area of the square = side^2.
The side length is given as √(9/4).
Area of the square = (√(9/4))^2 = (3/2)^2 = 2.25.
Therefore, the area of the square box is 2.25 square units.
A square-shaped building measuring 9/4 square meters is built; if each of the sides is √(9/4), what will be the square meters of half of the building?
1.125 square meters
We can just divide the given area by 2 as the building is square-shaped.
Dividing 9/4 by 2 gives us 1.125.
So half of the building measures 1.125 square meters.
Calculate √(9/4) × 5.
7.5
The first step is to find the square root of 9/4, which is 3/2 or 1.5.
The second step is to multiply 1.5 by 5.
So 1.5 × 5 = 7.5.
What will be the square root of (9 + 1)?
The square root is 3.162
To find the square root, we need to find the sum of (9 + 1).
9 + 1 = 10, and then √10 ≈ 3.162.
Therefore, the square root of (9 + 1) is approximately ±3.162.
Find the perimeter of a rectangle if its length ‘l’ is √(9/4) units and the width ‘w’ is 5 units.
The perimeter of the rectangle is 13 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(9/4) + 5) = 2 × (1.5 + 5) = 2 × 6.5 = 13 units.
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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