Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots have applications in various fields such as engineering, finance, and more. Here, we will discuss the square root of 1192.
The square root is the inverse of squaring a number. 1192 is not a perfect square. The square root of 1192 is expressed in both radical and exponential form. In the radical form, it is expressed as √1192, whereas in exponential form it is expressed as (1192)^(1/2). √1192 ≈ 34.527, 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.
For perfect square numbers, the prime factorization method is used. However, for non-perfect square numbers like 1192, the long division method and approximation method are used. Let us learn about these methods:
Prime factorization involves expressing a number as a product of its prime factors. Let us look at how 1192 is broken down:
Step 1: Find the prime factors of 1192 Breaking it down, we get 2 x 2 x 2 x 149: 2^3 x 149
Step 2: Now that we have the prime factors of 1192, the next step is to attempt pairing. Since 1192 is not a perfect square, the digits cannot be perfectly paired.
Therefore, calculating 1192 using prime factorization is not feasible.
The long division method is useful for non-perfect square numbers. Here's how to use it to find the square root of 1192:
Step 1: Group the numbers from right to left. For 1192, group as 92 and 11.
Step 2: Find n whose square is ≤ 11. We can use n = 3 because 3^2 = 9, which is less than 11. Subtract 9 from 11, leaving a remainder of 2.
Step 3: Bring down 92, making the new dividend 292. The new divisor is 2n = 6.
Step 4: Find n such that 6n x n ≤ 292. Using n = 4, 64 x 4 = 256, which is less than 292.
Step 5: Subtract 256 from 292, leaving a remainder of 36.
Step 6: Add a decimal point to continue. Bring down two zeros to make 3600.
Step 7: The new divisor is 68. Find n such that 68n x n ≤ 3600. Using n = 5, 685 x 5 = 3425.
Step 8: Subtract 3425 from 3600, leaving a remainder of 175.
Step 9: The quotient is 34.5. Continue these steps until the desired decimal precision is achieved.
The approximation method is another way to find square roots:
Step 1: Identify the closest perfect squares around √1192. The smaller perfect square is 1156 (34^2), and the larger is 1225 (35^2). So, √1192 is between 34 and 35.
Step 2: Use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Applying the formula: (1192 - 1156) / (1225 - 1156) ≈ 0.527
Add this decimal to the integer part: 34 + 0.527 = 34.527
Students often make mistakes when finding square roots, such as ignoring the negative square root, skipping steps in the long division method, etc. Let's explore some common mistakes:
Can you help Max find the area of a square box if its side length is given as √1192?
The area of the square is approximately 1192 square units.
The area of a square = side^2.
The side length is given as √1192.
Area = (√1192)^2 = 1192.
Therefore, the area of the square box is 1192 square units.
A square-shaped building measuring 1192 square feet is built; if each of the sides is √1192, what will be the square feet of half of the building?
596 square feet
Since the building is square-shaped, we can divide the area by 2.
Dividing 1192 by 2, we get 596.
So, half of the building measures 596 square feet.
Calculate √1192 x 5.
Approximately 172.635
First, find the square root of 1192, which is approximately 34.527.
Then multiply 34.527 by 5.
34.527 x 5 ≈ 172.635.
What will be the square root of (1192 + 8)?
The square root is approximately 35.
First, find the sum: 1192 + 8 = 1200.
Then find the square root of 1200.
√1200 ≈ 34.641.
So, the square root of (1192 + 8) is approximately ±34.641.
Find the perimeter of the rectangle if its length l is √1192 units and the width w is 38 units.
The perimeter of the rectangle is approximately 145.054 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1192 + 38)
= 2 × (34.527 + 38)
= 2 × 72.527
≈ 145.054 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.
: He loves to play the quiz with kids through algebra to make kids love it.