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 1189.
The square root is the inverse of the square of the number. 1189 is not a perfect square. The square root of 1189 is expressed in both radical and exponential form. In radical form, it is expressed as √1189, whereas in exponential form it is (1189)^(1/2). √1189 ≈ 34.49334, 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 like 1189, the prime factorization method is not applicable. Instead, the long division method and approximation method are used. Let us now learn these methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 1189 is broken down into its prime factors.
Step 1: Finding the prime factors of 1189 Breaking it down, we get 1189 = 13 x 91 = 13 x 7 x 13: 13^2 x 7
Step 2: We found the prime factors of 1189. However, since 1189 is not a perfect square, the digits of the number cannot be grouped into pairs.
Therefore, calculating √1189 using prime factorization might not be straightforward.
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 1189, we group it as 89 and 11.
Step 2: Now, we need to find n whose square is less than or equal to the leftmost group. For 11, n is 3 because 3 x 3 = 9 which is less than 11. The quotient is 3 and the remainder is 11 - 9 = 2.
Step 3: Bring down the next pair 89, making the new dividend 289. Add the old divisor with the same number 3 + 3 to get 6 as the new divisor.
Step 4: Find n such that 6n x n is less than or equal to 289. Let n be 4, then 64 x 4 = 256.
Step 5: Subtract 256 from 289; the difference is 33, and the quotient is 34.
Step 6: Since the dividend is less than the divisor, add a decimal point to the quotient. Adding the decimal point allows us to bring down two zeroes, making the new dividend 3300.
Step 7: Find a new divisor. The divisor is now 34 + 34 = 68. Find n such that 68n x n ≤ 3300. Let n be 4, then 684 x 4 = 2736.
Step 8: Subtract 2736 from 3300, resulting in 564.
Step 9: Bring down another pair of zeroes, making the dividend 56400.
Step 10: Continue this process.
The square root of 1189 is approximately 34.49.
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Let us learn how to find the square root of 1189 using the approximation method.
Step 1: Find the closest perfect squares around 1189. The closest perfect squares are 1156 (34^2) and 1225 (35^2). √1189 falls between 34 and 35.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (1189 - 1156) / (1225 - 1156) = 33/69 ≈ 0.478 Add this value to 34 (the square root of the nearest smaller perfect square): 34 + 0.478 ≈ 34.478
So, the square root of 1189 is approximately 34.478.
Students make mistakes while finding the square root, such as forgetting about the negative square root, skipping the long division method, etc. Let us look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √1189?
The area of the square is approximately 1416.5 square units.
The area of the square = side^2.
The side length is given as √1189.
Area of the square = side^2 = √1189 × √1189 ≈ 34.49334 × 34.49334 ≈ 1416.5.
Therefore, the area of the square box is approximately 1416.5 square units.
A square-shaped building measuring 1189 square feet is built; if each of the sides is √1189, what will be the square feet of half of the building?
594.5 square feet
We can divide the given area by 2 as the building is square-shaped.
Dividing 1189 by 2 gives us 594.5.
So, half of the building measures 594.5 square feet.
Calculate √1189 × 5.
Approximately 172.4667
First, find the square root of 1189, which is approximately 34.49334.
Multiply this by 5.
So, 34.49334 × 5 ≈ 172.4667.
What will be the square root of (1189 + 36)?
The square root is approximately 35.
To find the square root, sum 1189 + 36.
1189 + 36 = 1225, and √1225 = 35.
Therefore, the square root of (1189 + 36) is ±35.
Find the perimeter of a rectangle if its length ‘l’ is √1189 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 145.9867 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1189 + 38)
≈ 2 × (34.49334 + 38)
= 2 × 72.49334
≈ 145.9867 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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