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 9500.
The square root is the inverse of the square of the number. 9500 is not a perfect square. The square root of 9500 is expressed in both radical and exponential form. In the radical form, it is expressed as √9500, whereas in exponential form it is expressed as (9500)^(1/2). √9500 ≈ 97.4679, 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; instead, 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 9500 is broken down into its prime factors.
Step 1: Finding the prime factors of 9500
Breaking it down, we get 2 x 2 x 5 x 5 x 5 x 19: 2^2 x 5^3 x 19
Step 2: Now we have found the prime factors of 9500. The next step is to make pairs of those prime factors. Since 9500 is not a perfect square, the digits of the number cannot be grouped in perfect pairs. Therefore, calculating √9500 using prime factorization alone is not possible.
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 9500, we need to group it as 00 and 95.
Step 2: Now we need to find n whose square is less than or equal to 95. We can say n is 9 because 9 x 9 = 81, which is less than 95. Now the quotient is 9, and after subtracting 81 from 95, the remainder is 14.
Step 3: Bring down the next pair, which is 00, making the new dividend 1400. Add the old divisor with the same number 9 + 9, which gives us 18, the new divisor.
Step 4: Now, we need to find a digit x for which 18x × x ≤ 1400. Trying x = 7 gives us 187 x 7 = 1309.
Step 5: Subtract 1309 from 1400, resulting in a remainder of 91.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down pairs of zeroes.
Step 7: Continue these steps until you have a sufficiently accurate result.
The square root of 9500 using long division is approximately 97.4679.
The approximation method is another method for finding square roots; it is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 9500 using the approximation method.
Step 1: Find the closest perfect squares to 9500. The closest perfect square below 9500 is 9409 (which is 97^2) and above it is 9604 (which is 98^2). So √9500 is between 97 and 98.
Step 2: Use linear interpolation to estimate √9500. Using the formula: (9500 - 9409) / (9604 - 9409) = 0.4725 Adding this value to the lower estimate, we have 97 + 0.4725 = 97.4725.
So the square root of 9500 is approximately 97.4725.
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 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 √9500?
The area of the square is 9500 square units.
The area of a square is given by side^2.
The side length is given as √9500.
Area of the square = (√9500)^2 = 9500 square units.
A square-shaped building measures 9500 square feet in area; if each of the sides is √9500, what will be the area of half of the building?
4750 square feet
To find the area of half the building, divide the total area by 2.
9500 / 2 = 4750
So half of the building measures 4750 square feet.
Calculate √9500 x 5.
487.3395
The first step is to find the square root of 9500, which is approximately 97.4679.
The second step is to multiply 97.4679 by 5.
So, 97.4679 x 5 ≈ 487.3395
What will be the square root of (9500 + 100)?
The square root is approximately 98.4886
To find the square root, we need to find the sum of (9500 + 100). 9500 + 100 = 9600, and then √9600 ≈ 98.4886.
Find the perimeter of a rectangle if its length ‘l’ is √9500 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 294.9358 units.
The perimeter of a rectangle is given by 2 × (length + width).
Perimeter = 2 × (√9500 + 50) = 2 × (97.4679 + 50) ≈ 2 × 147.4679 = 294.9358 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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