127 LearnersLast updated on May 26th, 2025
Square Root of 2975
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 2975.
What is the Square Root of 2975?
The square root is the inverse of the square of the number. 2975 is not a perfect square. The square root of 2975 is expressed in both radical and exponential form. In the radical form, it is expressed as √2975, whereas (2975)^(1/2) in the exponential form. √2975 ≈ 54.539, 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.
Finding the Square Root of 2975
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2975 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2975 is broken down into its prime factors:
Step 1: Finding the prime factors of 2975 Breaking it down, we get 5 x 5 x 11 x 11: 5^2 x 11^2
Step 2: Now we found out the prime factors of 2975. The next step is to make pairs of those prime factors. Since 2975 is not a perfect square, no complete pairs can be made.
Therefore, calculating √2975 using prime factorization without further approximation is not possible.
Square Root of 2975 by Long Division Method
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 2975, we group it as 75 and 29.
Step 2: Now we need to find n whose square is closest to 29. We can say n as '5' because 5 x 5 = 25, which is less than or equal to 29. Now the quotient is 5 and the remainder is 4.
Step 3: Bring down 75, making it the new dividend (475). Add the old divisor with the same number (5 + 5 = 10) to get the new divisor (10).
Step 4: Find n such that (10n) x n is less than or equal to 475. Let us consider n as 4; now 104 x 4 = 416.
Step 5: Subtract 416 from 475 to get a remainder of 59, and the quotient becomes 54.
Step 6: Since the dividend is less than the divisor, add a decimal point and two zeroes to the dividend. Now the new dividend is 5900.
Step 7: Find the new divisor. Let n be 5; then 1095 x 5 = 5475.
Step 8: Subtracting 5475 from 5900 gives 425.
Step 9: Continue these steps until you reach the desired precision.
So the approximate square root of √2975 is 54.539.
Square Root of 2975 by Approximation Method
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 2975 using the approximation method.
Step 1: Find the closest perfect squares to √2975. The smallest perfect square less than 2975 is 2916 (54^2) and the largest perfect square greater than 2975 is 3025 (55^2). √2975 falls between 54 and 55.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (2975 - 2916) / (3025 - 2916) = 59 / 109 ≈ 0.541 Adding this decimal to 54 gives us 54 + 0.541 = 54.541.
Thus, the square root of 2975 is approximately 54.541.
Common Mistakes and How to Avoid Them in the Square Root of 2975
Students often make mistakes while finding the square root, 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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example, √50 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before proceeding.
For example, √(12+24) ≠ √12 + √24. The right way is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value
For example, √50 ≠ 7. The correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, resulting in a wrong answer at the end of the sum. This may occur during subtraction or elsewhere.
Square Root of 2975 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2975?
The area of the square is approximately 2975 square units.
Explanation
The area of the square = side^2.
The side length is given as √2975.
Area of the square = side^2 = √2975 x √2975 = 2975.
Therefore, the area of the square box is approximately 2975 square units.
Problem 2
A square-shaped building measuring 2975 square feet is built; if each of the sides is √2975, what will be the square feet of half of the building?
1487.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2975 by 2 gives us 1487.5.
So half of the building measures 1487.5 square feet.
Problem 3
Calculate √2975 x 5.
272.695
Explanation
The first step is to find the square root of 2975, which is approximately 54.539.
The second step is to multiply 54.539 by 5.
So 54.539 x 5 = 272.695.
Problem 4
What will be the square root of (2975 + 25)?
The square root is 55.
Explanation
To find the square root, we need to find the sum of (2975 + 25).
2975 + 25 = 3000, and then √3025 = 55.
Therefore, the square root of (2975 + 25) is ±55.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2975 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 209.078 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2975 + 50)
= 2 × (54.539 + 50)
= 2 × 104.539
= 209.078 units.
FAQ on Square Root of 2975
1.What is √2975 in its simplest form?
2.Mention the factors of 2975.
3.Calculate the square of 2975.
4.Is 2975 a prime number?
5.2975 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 2975?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 2975?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 2975
- Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime numbers. For example, the prime factorization of 2975 is 5 x 5 x 11 x 11.
- Approximation: A method to find an estimated value of a number or measurement. It is often used to find the square root of non-perfect squares.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
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