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 like vehicle design, finance, etc. Here, we will discuss the square root of 36/16.
The square root is the inverse of the square of a number. 36/16 can be simplified to 9/4, which is a perfect square. The square root of 36/16 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(36/16), whereas (36/16)^(1/2) in the exponential form. √(36/16) = 3/2 or 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 prime factorization method is used for perfect square numbers. Since 36/16 simplifies to a perfect square, we can use the prime factorization method directly. Let us now learn the following methods to verify the result:
The product of prime factors is the prime factorization of a number. Now let us look at how 36/16 is broken down into its prime factors.
Step 1: Simplify 36/16 to 9/4.
Step 2: Find the prime factors of 9 and 4: 9 = 3 x 3 4 = 2 x 2
Step 3: Now, take the square root of both the numerator and the denominator: √(9/4) = √9 / √4 = 3/2.
Thus, the square root of 36/16 is 3/2.
The simplification method involves simplifying the fraction first and then finding the square root. Let us now learn how to find the square root using the simplification method, step by step.
Step 1: Simplify the fraction 36/16 to 9/4.
Step 2: Calculate the square root of the simplified fraction: √(9/4) = √9 / √4 = 3/2.
So, the square root of 36/16 is 3/2 or 1.5.
The rationalization method is useful for expressing the square root in a simplified manner. Now let us learn how to find the square root of 36/16 using the rationalization method.
Step 1: Simplify the fraction 36/16 to 9/4.
Step 2: Since 9/4 is a perfect square, directly find the square root: √(9/4) = 3/2.
Thus, the square root of 36/16 is 3/2 or 1.5.
Students can make mistakes while finding the square root, such as not simplifying fractions first or confusing rational numbers with irrational ones. Now let's look at a few of those mistakes in detail.
Can you help Lisa find the area of a square if its side length is given as √(36/16)?
The area of the square is 2.25 square units.
The area of the square = side².
The side length is given as √(36/16) = 3/2.
Area of the square = (3/2)² = 3/2 × 3/2 = 9/4 = 2.25.
Therefore, the area of the square is 2.25 square units.
A square-shaped garden measuring 36/16 square meters is built; if each of the sides is √(36/16), what will be the square meters of half of the garden?
1.125 square meters
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 36/16 by 2 = 9/8 = 1.125.
So half of the garden measures 1.125 square meters.
Calculate √(36/16) × 8.
12
The first step is to find the square root of 36/16 which is 1.5, the second step is to multiply 1.5 with 8.
So 1.5 × 8 = 12.
What will be the square root of (36 + 16)?
The square root is 7.
To find the square root, we need to find the sum of (36 + 16).
36 + 16 = 52, and then √52 ≈ 7.211.
Therefore, the square root of (36 + 16) is approximately ±7.211.
Find the perimeter of a rectangle if its length ‘l’ is √(36/16) units and the width ‘w’ is 4 units.
The perimeter of the rectangle is 11 units.
Perimeter of the rectangle = 2 × (length + width).
Length = √(36/16) = 1.5 units.
Perimeter = 2 × (1.5 + 4)
= 2 × 5.5
= 11 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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