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 183.
The square root is the inverse of the square of the number. 183 is not a perfect square. The square root of 183 is expressed in both radical and exponential form. In the radical form, it is expressed as √183, whereas in the exponential form, it is expressed as (183)^(1/2). √183 ≈ 13.5277, 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 183, the 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 183 is broken down into its prime factors.
Step 1: Finding the prime factors of 183 Breaking it down, we get 3 x 61, which are both prime numbers: 3^1 x 61^1
Step 2: Now we have found the prime factors of 183. Since 183 is not a perfect square, these factors cannot form a pair.
Therefore, calculating 183 using prime factorization is not feasible for finding an exact square root.
The long division method is used for non-perfect square numbers. In this method, we should find the closest perfect square number to the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Begin by grouping the digits of 183 starting from the right. We have 83 and 1 as grouped numbers.
Step 2: Find a number whose square is less than or equal to 1. Here, 1^2 = 1 fits. Thus, the quotient is 1, and the remainder is 0 after subtracting 1 from 1.
Step 3: Bring down 83, making the new dividend 83. Add the old divisor and the quotient: 1 + 1 = 2, which becomes part of the new divisor.
Step 4: Determine the next number n such that 2n × n is less than or equal to 83. Trying n = 3 gives 23 × 3 = 69.
Step 5: Subtract 69 from 83, giving a remainder of 14. The quotient is now 13.
Step 6: Add a decimal point to the quotient and bring down 00 to the remainder, making it 1400.
Step 7: Find the new divisor: 26n, where n = 5, gives 265 × 5 = 1325.
Step 8: Subtract 1325 from 1400, yielding a remainder of 75. The quotient is now 13.5.
Step 9: Continue the process until you reach the desired accuracy.
The square root of 183 is approximately 13.53.
The approximation method is an easy method for finding square roots. Let us learn how to find the square root of 183 using this method.
Step 1: Identify the closest perfect squares around √183. The smallest perfect square less than 183 is 169, and the largest perfect square greater than 183 is 196. Therefore, √183 is between 13 and 14.
Step 2: Use interpolation to find a closer estimate. The formula is: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using the formula: (183 - 169) / (196 - 169) = 14 / 27 ≈ 0.5185
Step 3: Add this decimal to the smaller perfect square root: 13 + 0.5185 ≈ 13.52, so the square root of 183 is approximately 13.52.
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's explore some common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √183?
The area of the square is approximately 183 square units.
The area of the square = side².
The side length is given as √183.
Area of the square = side² = √183 × √183 = 183.
Therefore, the area of the square box is approximately 183 square units.
A square-shaped garden measures 183 square meters. If each of the sides is √183 meters, what will be the area of half of the garden?
91.5 square meters
To find half the area of the garden, divide the total area by 2. 183 ÷ 2 = 91.5
So half of the garden measures 91.5 square meters.
Calculate √183 × 4.
54.11
First, find the square root of 183, which is approximately 13.53.
Then multiply 13.53 by 4. 13.53 × 4 = 54.11
What is the square root of (183 - 3)?
The square root is 13.
To find the square root, first calculate (183 - 3) = 180. The square root of 180 is approximately 13.42.
Therefore, the square root of (183 - 3) is approximately 13.42, rounded to 13 for simplicity.
Find the perimeter of a rectangle if its length ‘l’ is √183 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 87.06 units.
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√183 + 20) = 2 × (13.53 + 20) ≈ 2 × 33.53 = 67.06 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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