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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 6561.
The square root is the inverse of the square of the number. 6561 is a perfect square. The square root of 6561 is expressed in both radical and exponential form. In the radical form, it is expressed as √6561, whereas (6561)^(1/2) in the exponential form. √6561 = 81, 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 6561, the prime factorization method is suitable. Additionally, the square root of perfect squares can be found directly. Let us now learn the following method: Prime factorization method
The product of prime factors is the prime factorization of a number. Now let us look at how 6561 is broken down into its prime factors. Step 1: Finding the prime factors of 6561 Breaking it down, we get 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3: 3^8 Step 2: Now we have found the prime factors of 6561. The next step is to make pairs of those prime factors. Since 6561 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √6561 = 3^4 = 81.
The long division method is another way to find the square root of perfect square numbers. However, since 6561 is a perfect square, we already know the square root is 81. Let us briefly outline the long division method for educational purposes: Step 1: We group the digits of 6561 starting from the right. Step 2: We find a number whose square is closest to or equal to 65, which is 8. Step 3: Subtracting 64 from 65, we get 1. Step 4: Bring down the next pair of digits (61). The new dividend is 161. Step 5: The divisor is now 16 (2*8). Step 6: Find n such that 16n * n ≤ 161. Here, n is 1. Step 7: Subtract 161 from 161, resulting in 0. Step 8: The quotient is 81, which is the square root of 6561.
The approximation method is not needed for perfect squares, but it can be used for understanding. For 6561, we recognize it as a perfect square, so the square root is exactly 81.
Students might make mistakes while finding the square root, such as confusing it with non-perfect squares or using incorrect methods. Let's look at a few common mistakes and their solutions:
Can you help Max find the area of a square box if its side length is given as √6561?
The area of the square is 6561 square units.
The area of the square = side^2. The side length is given as √6561. Area of the square = side^2 = √6561 x √6561 = 81 × 81 = 6561. Therefore, the area of the square box is 6561 square units.
A square-shaped building measuring 6561 square feet is built; if each of the sides is √6561, what will be the square feet of half of the building?
3280.5 square feet
We can divide the given area by 2 as the building is square-shaped. Dividing 6561 by 2 = 3280.5. So half of the building measures 3280.5 square feet.
Calculate √6561 x 5.
405
The first step is to find the square root of 6561, which is 81. The second step is to multiply 81 by 5. So 81 x 5 = 405.
What will be the square root of (6400 + 161)?
The square root is 81.
To find the square root, we need to find the sum of (6400 + 161). 6400 + 161 = 6561, and then √6561 = 81. Therefore, the square root of (6400 + 161) is ±81.
Find the perimeter of the rectangle if its length ‘l’ is √6561 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 238 units.
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√6561 + 38) = 2 × (81 + 38) = 2 × 119 = 238 units.
Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, that is √81 = 9. Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers. Perfect square: A perfect square is a number that has an integer as its square root. For example, 81 is a perfect square because √81 = 9. Prime factorization: Prime factorization is expressing a number as a product of its prime factors. Long division method: A method used to find the square root of a number by dividing and averaging.
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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