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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/81.
The square root is the inverse of the square of the number. 1/81 is a perfect square. The square root of 1/81 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(1/81), whereas (1/81)^(1/2) in the exponential form. √(1/81) = 1/9, 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 useful for finding the square roots of perfect squares. For non-perfect squares, methods such as long division and approximation are used. Since 1/81 is a perfect square, let's use the prime factorization method:
The prime factorization of a number involves expressing it as a product of its prime factors. Let us look at how 1/81 is broken down into its prime factors:
Step 1: Finding the prime factors of 81 Breaking it down, we get 3 × 3 × 3 × 3 = 3^4.
Step 2: Since 1 is a perfect square, it remains as is: 1 = 1^2.
Step 3: Pair the prime factors of the denominator. We can pair the factors into (3^2) × (3^2).
Step 4: The square root of each pair is 3, so the square root of the denominator is 3 × 3 = 9.
Step 5: Therefore, the square root of 1/81 is 1/9.
The long division method is commonly used for non-perfect square numbers, but it can also verify your result for perfect squares.
Step 1: Consider the numerator and denominator separately. The square root of 1 is 1.
Step 2: Apply the long division method for 81 to confirm that its square root is 9.
Step 3: Therefore, the square root of 1/81 is 1/9.
Students often make mistakes while finding square roots, such as forgetting about the negative square root or confusing it with cube roots. Let's explore some common errors and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √(1/81)?
The area of the square is 1/81 square units.
The area of the square = side^2.
The side length is given as √(1/81).
Area of the square = side^2 = (1/9) × (1/9) = 1/81.
Therefore, the area of the square box is 1/81 square units.
A square-shaped building measuring 1/81 square meters is built; if each of the sides is √(1/81), what will be the square meters of half of the building?
1/162 square meters
We can divide the given area by 2 as the building is square-shaped.
Dividing 1/81 by 2 = 1/162.
So half of the building measures 1/162 square meters.
Calculate √(1/81) × 5.
5/9
The first step is to find the square root of 1/81, which is 1/9. The second step is to multiply 1/9 by 5. So (1/9) × 5 = 5/9.
What will be the square root of (1/81 + 8)?
The square root is approximately 2.833.
To find the square root, we need to find the sum of (1/81 + 8).
1/81 + 8 = 8.012345.
Then the square root of 8.012345 is approximately 2.833.
Therefore, the square root of (1/81 + 8) is approximately ±2.833.
Find the perimeter of a rectangle if its length ‘l’ is √(1/81) units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 76.222 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(1/81) + 38) = 2 × (1/9 + 38) = 2 × (0.1111 + 38) = 2 × 38.1111 = 76.222 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.
: He loves to play the quiz with kids through algebra to make kids love it.