Last updated on May 26th, 2025
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 vehicle design, finance, etc. Here, we will discuss the square root of 81/100.
The square root is the inverse of the square of the number. 81/100 is a perfect square. The square root of 81/100 is expressed in both radical and exponential form. In the radical form, it is expressed as √(81/100), whereas (81/100)^(1/2) in the exponential form. √(81/100) = 9/10, 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. For non-perfect square numbers, methods like the long-division method and approximation method are used. However, since 81/100 is a perfect square, let's explore the prime factorization method:
The product of prime factors is the prime factorization of a number. Now let us look at how 81/100 is broken down into its prime factors.
Step 1: Finding the prime factors of 81 and 100 Breaking them down, we get 81 = 3 x 3 x 3 x 3 = 3^4 and 100 = 2 x 2 x 5 x 5 = 2^2 x 5^2
Step 2: Now we found out the prime factors of 81 and 100. Since both are perfect squares, we can take the square root of each separately. √(81/100) = √81 / √100 = 9/10
The long division method is generally used for non-perfect square numbers. However, for completeness, let's outline it here for 81/100.
Step 1: Since 81/100 is a fraction, find the square root of the numerator and the denominator separately.
Step 2: The square root of 81 is 9 and the square root of 100 is 10.
Step 3: Therefore, the square root of 81/100 is 9/10.
The approximation method is not needed for perfect squares, but we can briefly describe it here.
Step 1: Since 81/100 is a known perfect square, this method is not required. However, if it were not a perfect square, we would estimate between the nearest perfect squares.
Step 2: For 81/100, since it is a perfect square, the square root is exactly 9/10.
Students sometimes make mistakes while finding square roots, such as forgetting about the properties of fractions. Let's look at a few common mistakes.
Can you help Max find the area of a square box if its side length is given as √(81/100)?
The area of the square is 0.81 square units.
The area of the square = side^2.
The side length is given as √(81/100).
Area of the square = (√(81/100))^2 = (9/10) × (9/10) = 0.81
Therefore, the area of the square box is 0.81 square units.
A square-shaped plot measures 81/100 square meters; if each of the sides is √(81/100), what will be the square meters of half of the plot?
0.405 square meters
We can just divide the given area by 2 as the plot is square-shaped.
Dividing 0.81 by 2 = we get 0.405.
So half of the plot measures 0.405 square meters.
Calculate √(81/100) × 5.
4.5
The first step is to find the square root of 81/100, which is 9/10.
The second step is to multiply 9/10 with 5.
So (9/10) × 5 = 4.5.
What will be the square root of (81 + 19)?
The square root is 10.
To find the square root, we need to find the sum of (81 + 19). 81 + 19 = 100, and then √100 = 10.
Therefore, the square root of (81 + 19) is ±10.
Find the perimeter of the rectangle if its length ‘l’ is √(81/100) units and the width ‘w’ is 1 unit.
We find the perimeter of the rectangle as 2.8 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(81/100) + 1) = 2 × (0.9 + 1) = 2 × 1.9 = 3.8 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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