123 LearnersLast updated on May 26th, 2025
Square Root of 605
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 605.
What is the Square Root of 605?
The square root is the inverse of the square of the number. 605 is not a perfect square. The square root of 605 is expressed in both radical and exponential forms. In the radical form, it is expressed as √605, whereas in exponential form it is (605)^(1/2). √605 ≈ 24.5972, 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 605
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 605 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 605 is broken down into its prime factors:
Step 1: Finding the prime factors of 605 Breaking it down, we get 5 × 11 × 11: 5^1 × 11^2
Step 2: Now we found out the prime factors of 605. The second step is to make pairs of those prime factors. Since 605 is not a perfect square, all prime factors cannot be perfectly paired. Therefore, calculating 605 using prime factorization will not yield an exact whole number square root.
Square Root of 605 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 605, we need to group it as 05 and 6.
Step 2: Now we need to find n whose square is closest to 6. We can say n as ‘2’ because 2 × 2 = 4, which is lesser than or equal to 6. The quotient is 2, subtracting 4 from 6 gives the remainder 2.
Step 3: Now let us bring down 05 to make the new dividend 205. Add the old divisor with the same number 2 + 2, we get 4 which will be our new divisor.
Step 4: Now we get 4n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 205. Let us consider n as 5, now 4 × 5 × 5 = 100.
Step 6: Subtract 100 from 205, the difference is 105, and the quotient is 25.
Step 7: Since the dividend is more than the divisor, we continue with decimal places. Add a decimal point and bring down two zeroes to the dividend, making it 10500.
Step 8: Now we need to find the new divisor, 495, because 495 × 2 = 990.
Step 9: Subtracting 990 from 1050 gives a remainder of 1050.
Step 10: The quotient becomes 24.5.
Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero. So the square root of √605 is approximately 24.60.
Square Root of 605 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 605 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √605. The smallest perfect square less than 605 is 576, and the largest perfect square greater than 605 is 625. √605 falls somewhere between 24 and 25.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (605 - 576) ÷ (625 - 576) = 29 ÷ 49 ≈ 0.59. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 24 + 0.59 = 24.59, so the square root of 605 is approximately 24.59.
Common Mistakes and How to Avoid Them in the Square Root of 605
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07; there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For Example: √(12 + 24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For Example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For Example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the problem. This may either happen in subtraction or elsewhere.
Square Root of 605 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √605?
The area of the square is approximately 605 square units.
Explanation
The area of the square = side^2. The side length is given as √605. Area of the square = side^2 = √605 × √605 = 605. Therefore, the area of the square box is approximately 605 square units.
Problem 2
A square-shaped building measuring 605 square feet is built; if each of the sides is √605, what will be the square feet of half of the building?
302.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 605 by 2 = we get 302.5. So half of the building measures 302.5 square feet.
Problem 3
Calculate √605 × 5.
Approximately 122.99
Explanation
The first step is to find the square root of 605, which is approximately 24.60. The second step is to multiply 24.60 with 5. So 24.60 × 5 = 123.
Problem 4
What will be the square root of (576 + 29)?
The square root is 25.
Explanation
To find the square root, we need to find the sum of (576 + 29). 576 + 29 = 605, and then √605 ≈ 24.60. Therefore, the square root of (576 + 29) is approximately 24.60.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √605 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 89.2 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√605 + 20) = 2 × (24.60 + 20) = 2 × 44.60 = 89.2 units.
FAQ on Square Root of 605
1.What is √605 in its simplest form?
2.Mention the factors of 605.
3.Calculate the square of 605.
4.Is 605 a prime number?
5.605 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 605?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 605?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 605
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, 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, it is always the positive square root that is used more often due to its significance in the real world. That is why it is also known as the principal square root.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long Division Method: This is a method used to find the square root of a non-perfect square number by performing division through a series of steps to find the square root value.
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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.
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