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 fields such as architecture, finance, and engineering. Here, we will discuss the square root of 60.
The square root is the inverse of the square of a number. 60 is not a perfect square. The square root of 60 is expressed in both radical and exponential form. In the radical form, it is expressed as √60, whereas (60)^(1/2) in the exponential form. √60 ≈ 7.74597, 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.
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long-division method and approximation method are used. Let us now learn the following methods: - Prime factorization method
The product of prime factors is the prime factorization of a number. Now let us look at how 60 is broken down into its prime factors.
Step 1: Finding the prime factors of 60
Breaking it down, we get 2 x 2 x 3 x 5: 2^2 x 3^1 x 5^1
Step 2: Now we found out the prime factors of 60. The second step is to make pairs of those prime factors. Since 60 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √60 using prime factorization gives us 2√15, which is an irrational number.
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 60, we need to group it as 60.
Step 2: Now we need to find n whose square is less than or equal to 60. We can say n as ‘7’ because 7 x 7 = 49, which is less than 60. Now the quotient is 7, and the remainder is 60 - 49 = 11.
Step 3: Now let us bring down 00, which makes the new dividend 1100.
Step 4: Double the divisor (7) and write it as 14.
Step 5: We need to find a digit x such that 14x x x ≤ 1100. Trying x = 7 gives us 1447 x 7 = 10129, which is too large. Trying x = 6 gives us 146 x 6 = 876, which fits.
Step 6: Subtract 876 from 1100, which gives 224.
Step 7: Since the remainder is not zero, continue the process with the new dividend 22400 and new divisor 1460.
Step 8: The next x is found similarly. After a few more steps, we calculate the square root of 60 as approximately 7.74.
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 60 using the approximation method.
Step 1: Now we have to find the closest perfect squares of 60. The smallest perfect square less than 60 is 49 (7^2), and the largest perfect square greater than 60 is 64 (8^2). √60 falls somewhere between 7 and 8.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square). Going by the formula (60 - 49) / (64 - 49) = 11/15 ≈ 0.733
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 7 + 0.733 = 7.733, so the square root of 60 is approximately 7.73.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √60?
The area of the square is approximately 60 square units.
The area of the square = side².
The side length is given as √60.
Area of the square = (√60)² = 60.
Therefore, the area of the square box is approximately 60 square units.
A square-shaped building measuring 60 square feet is built; if each of the sides is √60, what will be the square feet of half of the building?
30 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 60 by 2, we get 30.
So half of the building measures 30 square feet.
Calculate √60 × 5.
Approximately 38.73
The first step is to find the square root of 60, which is approximately 7.74597.
The second step is to multiply 7.74597 by 5.
So 7.74597 × 5 ≈ 38.73.
What will be the square root of (56 + 4)?
The square root is 8.
To find the square root, we need to find the sum of (56 + 4). 56 + 4 = 60, and then √60 = approximately ±7.74597.
Therefore, the square root of (56 + 4) is approximately 7.74597.
Find the perimeter of the rectangle if its length ‘l’ is √60 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 55.49 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√60 + 20) ≈ 2 × (7.74597 + 20) ≈ 2 × 27.74597 ≈ 55.49 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.
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