102 LearnersLast updated on May 26th, 2025
Square Root of 60.37
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 60.37.
What is the Square Root of 60.37?
The square root is the inverse of the square of the number. 60.37 is not a perfect square. The square root of 60.37 is expressed in both radical and exponential forms. In the radical form, it is expressed as √60.37, whereas (60.37)^(1/2) is in exponential form. √60.37 ≈ 7.7712, 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 60.37
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 60.37 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, since 60.37 is not an integer, traditional prime factorization is not directly applicable. Instead, we focus on approximation and long division methods for non-perfect squares like 60.37.
Square Root of 60.37 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Start by grouping the digits of 60.37 from right to left as 60 and 37.
Step 2: Find the largest number whose square is less than or equal to 60. That number is 7 since 7 x 7 = 49. Subtract 49 from 60, leaving a remainder of 11.
Step 3: Bring down 37, making the new dividend 1137. Double the quotient (7), giving us 14 as the new divisor prefix.
Step 4: Find the largest digit (n) such that 14n × n ≤ 1137. The appropriate n is 8.
Step 5: Subtract 1144 from 1137 to get a remainder of -7. Adjust calculations due to negative results, refine to get a more accurate divisor.
Step 6: Repeat these steps to further decimal places for more precision in the result.
So the approximate square root of √60.37 is 7.7712.
Square Root of 60.37 by Approximation Method
The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Let's approximate the square root of 60.37 using the closest perfect squares.
Step 1: Identify the perfect squares nearest to 60.37. The closest lower perfect square is 49, and the closest higher perfect square is 64. √60.37 falls between √49 (7) and √64 (8).
Step 2: Use linear approximation: (60.37 - 49) / (64 - 49) = 0.758.
Step 3: Add this approximation to the lower bound: 7 + 0.758 ≈ 7.758. Further refinement leads to 7.7712.
Therefore, the approximate square root of 60.37 is 7.7712.
Common Mistakes and How to Avoid Them in the Square Root of 60.37
Students often make mistakes while finding square roots, such as forgetting about the negative square root or misapplying methods. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. We typically use only the positive square root, as it is the required one for most real-world applications.
For example, √60.37 ≈ 7.7712, but there is also -7.7712.
Square root of 60.37 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √50?
The area of the square is 50 square units.
Explanation
The area of the square = side^2.
The side length is given as √50
Area of the square = √50 × √50 = 50.
Therefore, the area of the square box is 50 square units.
Problem 2
A square-shaped building measuring 60.37 square feet is built; if each of the sides is √60.37, what will be the square feet of half of the building?
30.185 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped
Dividing 60.37 by 2 gives 30.185.
So half of the building measures 30.185 square feet.
Problem 3
Calculate √60.37 × 5.
38.856
Explanation
The first step is to find the square root of 60.37, which is approximately 7.7712.
Multiply 7.7712 by 5. So 7.7712 × 5 ≈ 38.856.
Problem 4
What will be the square root of (50 + 10)?
The square root is 8.
Explanation
To find the square root, we need to find the sum of (50 + 10), which equals 60.
The nearest perfect square to 60 is approximately 8 (since 8 × 8 = 64).
Therefore, the square root of (50 + 10) is approximately 8.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √50 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 34.142 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√50 + 10) ≈ 2 × (7.071 + 10) = 2 × 17.071 ≈ 34.142 units.
FAQ on Square Root of 60.37
1.What is √60.37 in its simplest form?
2.Calculate the square of 60.37.
3.Is 60.37 a perfect square?
4.What is an irrational number?
5.What are the closest perfect squares to 60.37?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 60.37?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 60.37?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 60.37
- Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a fraction p/q, where q is not equal to zero, and p and q are integers.
- Approximation: Approximating involves finding a value close to the exact answer, often used in cases involving irrational numbers.
- Long division method: A step-by-step method used to find the square root of non-perfect squares.
- Decimal: A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.7712.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
