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 vehicle design, finance, etc. Here, we will discuss the square root of 1196.
The square root is the inverse of the square of the number. The number 1196 is a perfect square. The square root of 1196 is expressed in both radical and exponential form. In the radical form, it is expressed as √1196, whereas in the exponential form it is expressed as (1196)^(1/2). √1196 = 34, which is a rational number because it can 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. For non-perfect square numbers, methods such as long-division and approximation may be 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 1196 is broken down into its prime factors.
Step 1: Finding the prime factors of 1196. Breaking it down, we get 2 x 2 x 13 x 23 = 2² x 13 x 23.
Step 2: Now we found out the prime factors of 1196. The second step is to make pairs of those prime factors. Since 1196 is a perfect square, we can pair the factors as follows: (2×2) × (13) × (23).
Step 3: Take one factor from each pair and multiply them: 2 × 13 = 26.
Thus, the square root of 1196 using prime factorization is 34.
The long division method is particularly used for both perfect and non-perfect square numbers. 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 pairs of two. In the case of 1196, we can group it as 11 and 96.
Step 2: Now we need to find a number whose square is less than or equal to 11. We can say this number is 3 because 3 x 3 = 9, which is less than 11. Subtract 9 from 11 to get 2. Now, bring down the next pair (96), making the new dividend 296.
Step 3: Double the divisor (3) to get 6, and assume the new number is 6n. Find n such that 6n×n is less than or equal to 296. In this case, n is 4 because 64×4 = 256.
Step 4: Subtract 256 from 296 to get 40. Since we have no more pairs to bring down, we conclude the quotient as 34.
So the square root of √1196 is 34.
The approximation method can also be used to find the square roots, though it is more useful when dealing with non-perfect squares. Let's see how we find the square root of 1196 using this method.
Step 1: Identify the nearest perfect squares around 1196. The numbers 1156 (34²) and 1225 (35²) are perfect squares close to 1196.
Step 2: Since 1196 is already a perfect square and it falls exactly at 34, there's no need for approximation as the exact square root is 34.
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of these mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √1196?
The area of the square is 1196 square units.
The area of the square = side².
The side length is given as √1196.
Area of the square = side² = √1196 x √1196 = 34 x 34 = 1196.
Therefore, the area of the square box is 1196 square units.
A square-shaped building measuring 1196 square feet is built; if each of the sides is √1196, what will be the square feet of half of the building?
598 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1196 by 2 = 598.
So half of the building measures 598 square feet.
Calculate √1196 x 5.
170
The first step is to find the square root of 1196, which is 34.
The second step is to multiply 34 by 5.
So, 34 x 5 = 170.
What will be the square root of (1196 + 4)?
The square root is 35.
To find the square root, we need to find the sum of (1196 + 4).
1196 + 4 = 1200, and then √1200 = 34.64 (approx).
However, if we're looking for a perfect square, note that 34.64 is only an approximation.
Find the perimeter of the rectangle if its length ‘l’ is √1196 units and the width ‘w’ is 30 units.
We find the perimeter of the rectangle as 128 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1196 + 30)
= 2 × (34 + 30)
= 2 × 64
= 128 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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