103 LearnersLast updated on May 26th, 2025
Square Root of 495
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 the fields of vehicle design, finance, etc. Here, we will discuss the square root of 495.
What is the Square Root of 495?
The square root is the inverse of the square of a number. 495 is not a perfect square. The square root of 495 is expressed in both radical and exponential forms. In the radical form, it is expressed as √495, whereas in the exponential form it is expressed as (495)^(1/2). √495 ≈ 22.2486, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 495
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 495 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 495 is broken down into its prime factors:
Step 1: Finding the prime factors of 495 Breaking it down, we get 3 x 3 x 5 x 11: 3² x 5¹ x 11¹
Step 2: Now we have found the prime factors of 495. The second step is to make pairs of those prime factors. Since 495 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √495 using prime factorization is not straightforward.
Square Root of 495 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:
Step 1: To begin with, we need to group the numbers from right to left. In the case of 495, we need to group it as 95 and 4.
Step 2: Now we need to find n whose square is close to or less than 4. We can say n is ‘2’ because 2² is less than 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.
Step 3: Now let us bring down 95, which is the new dividend. Add the old divisor with the same number (2 + 2), and we get 4, which will be our new divisor.
Step 4: Now, we need to find a number n such that 4n × n ≤ 95. Let us consider n as 2, then 42 × 2 = 84.
Step 5: Subtract 84 from 95, and the difference is 11. The quotient is now 22.
Step 6: Add a decimal point to the quotient, allowing us to bring down two zeroes to the dividend. Now the new dividend is 1100.
Step 7: Find the new divisor, which is 444, because 444 × 2 = 888.
Step 8: Subtract 888 from 1100 to get the result 212.
Step 9: Continue doing these steps until we get two decimal places in the quotient. The final answer will be the approximate square root value.
So the square root of √495 is approximately 22.25.
Square Root of 495 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 495 using the approximation method.
Step 1: Now we have to find the closest perfect square of √495.
The smallest perfect square less than 495 is 484, and the largest perfect square greater than 495 is 529. √495 falls somewhere between 22 and 23.
Step 2: Now we need to apply the interpolation formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (495 - 484) ÷ (529 - 484) = 11 ÷ 45 ≈ 0.244. The approximate square root is 22 + 0.244 = 22.244, so the square root of 495 is approximately 22.244.
Common Mistakes and How to Avoid Them in the Square Root of 495
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we will typically use the positive square root.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 495 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √495?
The area of the square is 495 square units.
Explanation
The area of the square = side².
The side length is given as √495.
Area of the square = side² = √495 x √495 = 495.
Therefore, the area of the square box is 495 square units.
Problem 2
A square-shaped garden measuring 495 square feet is built; if each of the sides is √495, what will be the area of half of the garden?
247.5 square feet
Explanation
The area of the square garden is 495 square feet.
To find half of the area, divide by 2: 495 ÷ 2 = 247.5 square feet.
So, half of the garden measures 247.5 square feet.
Problem 3
Calculate √495 x 4.
Approximately 89
Explanation
First, find the square root of 495, which is approximately 22.248.
Then multiply 22.248 by 4: 22.248 x 4 ≈ 89.
So, √495 x 4 is approximately 89.
Problem 4
What will be the square root of (495 + 4)?
The square root is 23
Explanation
First, find the sum of (495 + 4): 495 + 4 = 499.
Since 499 is not a perfect square, approximate it:
The closest perfect square is 484 (22²) and 529 (23²). 499 is closer to 529, so the square root is approximately 23.
Therefore, the square root of (495 + 4) is approximately 23.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √495 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 144.4972 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√495 + 50).
First, find √495, which is approximately 22.248.
Perimeter = 2 × (22.248 + 50) = 2 × 72.248 = 144.4972 units.
Therefore, the perimeter of the rectangle is approximately 144.4972 units.
FAQ on Square Root of 495
1.What is √495 in its simplest form?
2.Mention the factors of 495.
3.Calculate the square of 495.
4.Is 495 a prime number?
5.495 is divisible by?
Important Glossaries for the Square Root of 495
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is commonly used due to its applications in the real world. This is known as the principal square root.
- Prime factorization:Breaking down a number into a product of prime numbers. For example, the prime factorization of 495 is 3 x 3 x 5 x 11.
- Decimal: A number that has a whole number and a fraction in a single representation. For example, 7.86, 8.65, and 9.42 are decimals.
Explore More algebra
Previous to Square Root of 495
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
