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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1058.
The square root is the inverse of the square of the number. 1058 is not a perfect square. The square root of 1058 is expressed in both radical and exponential form. In the radical form, it is expressed as √1058, whereas (1058)^(1/2) in the exponential form. √1058 ≈ 32.529, 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, 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:
The product of prime factors is the prime factorization of a number. Now let us look at how 1058 is broken down into its prime factors:
Step 1: Finding the prime factors of 1058 Breaking it down, we get 2 x 23 x 23: 2^1 x 23^2
Step 2: Now we found out the prime factors of 1058. Since 1058 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 1058 using prime factorization does not yield a whole number square root.
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 1058, we need to group it as 58 and 10.
Step 2: Now we need to find n whose square is less than or equal to 10. We can say n is ‘3’ because 3 × 3 = 9, which is less than 10. Now the quotient is 3, after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 58, making the new dividend 158. Add the old divisor with the same number 3 + 3 = 6, which will be part of our new divisor.
Step 4: The new divisor is 6n, and we need to find the value of n such that 6n × n ≤ 158. Let us consider n as 2, now 62 × 2 = 124.
Step 5: Subtracting 124 from 158 gives a remainder of 34, and the quotient is 32.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 3400.
Step 7: Now, continue the process to find decimal places.
The square root of 1058 is approximately 32.529.
Approximation method is another method for finding the square roots, and 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 1058 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √1058. The smallest perfect square less than 1058 is 1024 (32^2), and the largest perfect square greater than 1058 is 1089 (33^2). √1058 falls somewhere between 32 and 33.
Step 2: Now we approximate between these values. Since 1058 is closer to 1024, the square root will be closer to 32. Using a calculator or further steps.
We find the square root of 1058 is approximately 32.529.
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.
Can you help Max find the area of a square box if its side length is given as √1058?
The area of the square is 1058 square units.
The area of the square = side^2.
The side length is given as √1058.
Area of the square = side^2
= √1058 x √1058
= 1058.
Therefore, the area of the square box is 1058 square units.
A square-shaped building measuring 1058 square feet is built; if each of the sides is √1058, what will be the square feet of half of the building?
529 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1058 by 2 = we get 529.
So half of the building measures 529 square feet.
Calculate √1058 x 5.
162.645
The first step is to find the square root of 1058, which is approximately 32.529.
The second step is to multiply 32.529 by 5.
So 32.529 x 5 = 162.645.
What will be the square root of (1058 + 1)?
The square root is approximately 32.557.
To find the square root, we need to find the sum of (1058 + 1).
1058 + 1 = 1059, and then √1059 ≈ 32.557.
Therefore, the square root of (1058 + 1) is approximately ±32.557.
Find the perimeter of the rectangle if its length ‘l’ is √1058 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 165.058 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1058 + 50)
= 2 × (32.529 + 50)
= 2 × 82.529
≈ 165.058 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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