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 1168.
The square root is the inverse of the square of the number. 1168 is not a perfect square. The square root of 1168 is expressed in both radical and exponential form. In the radical form, it is expressed as √1168, whereas (1168)^(1/2) in the exponential form. √1168 ≈ 34.175, 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 and approximation methods 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 1168 is broken down into its prime factors.
Step 1: Finding the prime factors of 1168 Breaking it down, we get 2 x 2 x 2 x 2 x 73: 2^4 x 73^1
Step 2: Now we have found the prime factors of 1168. The second step is to make pairs of those prime factors. Since 1168 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 1168 using prime factorization is not possible to find an integer result.
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, group the numbers from right to left. In the case of 1168, we group it as 68 and 11.
Step 2: Now we need to find n whose square is close to or less than 11. We can say n is '3' because 3 x 3 = 9, which is lesser than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Bring down 68, which is the new dividend. Add the old divisor with the quotient, 3 + 3 = 6, which becomes the new divisor.
Step 4: We now have 26 as the new divisor. Find n such that 26n x n is less than or equal to 268.
Step 5: Let's consider n as 9, then 26 x 9 = 234
Step 6: Subtract 234 from 268; the difference is 34.
Step 7: 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 remainder. The new dividend is 3400.
Step 8: The new divisor becomes 68 (from 260 + 8) because 681 x 5 approximates 3400.
Step 9: Subtracting 3405 from 3400, we get a result of 5.
Step 10: Now the quotient is approximately 34.175.
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. Now let us learn how to find the square root of 1168 using the approximation method.
Step 1: Find the closest perfect squares around √1168. The closest perfect squares to 1168 are 1156 (34^2) and 1225 (35^2). √1168 falls between 34 and 35.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1168 - 1156) / (1225 - 1156) ≈ 0.175 Adding this to 34, we get 34 + 0.175 = 34.175. So, the square root of 1168 is approximately 34.175.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Here are some common mistakes and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √1168?
The area of the square is approximately 1363.89 square units.
The area of the square = side^2.
The side length is given as √1168.
Area of the square = side^2 = √1168 x √1168 ≈ 34.175 x 34.175 ≈ 1168.
Therefore, the area of the square box is approximately 1168 square units.
A square-shaped garden measuring 1168 square feet is built; if each of the sides is √1168, what will be the square feet of half of the garden?
584 square feet
We can divide the given area by 2 since the garden is square-shaped.
Dividing 1168 by 2, we get 584.
So, half of the garden measures 584 square feet.
Calculate √1168 x 5.
Approx. 170.875
The first step is to find the square root of 1168, which is approximately 34.175.
The second step is to multiply 34.175 by 5.
So, 34.175 x 5 ≈ 170.875.
What will be the square root of (1168 + 32)?
The square root is approximately 35.
To find the square root, we need to find the sum of (1168 + 32). 1168 + 32 = 1200, and then √1200 ≈ 34.64.
Therefore, the square root of (1168 + 32) is approximately 34.64.
Find the perimeter of the rectangle if its length ‘l’ is √1168 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 144.35 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1168 + 38) = 2 × (34.175 + 38) ≈ 2 × 72.175 ≈ 144.35 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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