127 LearnersLast updated on May 26th, 2025
Square Root of 4761
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 4761.
What is the Square Root of 4761?
The square root is the inverse of the square of the number. 4761 is a perfect square. The square root of 4761 is expressed in both radical and exponential form. In the radical form, it is expressed as √4761, whereas (4761)^(1/2) in the exponential form. √4761 = 69, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 4761
The prime factorization method is used for perfect square numbers. Since 4761 is a perfect square, we can use the prime factorization method to find its square root. Other methods, such as the long division method and approximation method, can also be used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4761 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4761 is broken down into its prime factors:
Step 1: Finding the prime factors of 4761
Breaking it down, we get 3 x 3 x 23 x 23: 3² x 23²
Step 2: Now we found out the prime factors of 4761. The second step is to make pairs of those prime factors. Since 4761 is a perfect square, the digits of the number can be grouped into pairs. Therefore, √4761 = 3 x 23 = 69.
Square Root of 4761 by Long Division Method
The long division method is particularly used for perfect and non-perfect square numbers. 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 4761, we need to group it as 47 and 61.
Step 2: Now we need to find n whose square is less than or equal to 47. We can say n is 6 because 6 x 6 = 36, which is less than 47. The quotient is 6, and the remainder is 47 - 36 = 11.
Step 3: Bring down 61 to make the new dividend 1161. Double the quotient (6) to get 12, which will be our new divisor.
Step 4: Find a digit m such that 12m x m is less than or equal to 1161. We find that m is 9 because 129 x 9 = 1161.
Step 5: Since there is no remainder, the quotient is 69. Therefore, the square root of 4761 is 69.
Square Root of 4761 by Approximation Method
The approximation method can be used to confirm the square root of a number. Since 4761 is a perfect square, approximation will confirm the result:
Step 1: We know that 4761 is between 3600 (60²) and 4900 (70²). Therefore, √4761 falls between 60 and 70.
Step 2: Calculate the midpoint: (60 + 70) / 2 = 65. Test squares around this point. Step 3: We find that 69 x 69 = 4761, confirming that the square root of 4761 is 69.
Common Mistakes and How to Avoid Them in the Square Root of 4761
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will typically take only the positive square root, as it is the required one.
For example: √50 = 7.07, 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 moving on to the next step.
For example: √(12 + 24) = √12 + √24 is a wrong method of using roots.
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 is wrong, the correct answer is √50 ≈ 7.071067.
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, which results in a wrong answer at the end of the sum. This may happen in subtraction or elsewhere.
Square Root of 4761 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4761?
The area of the square is 4761 square units.
Explanation
The area of the square = side².
The side length is given as √4761.
Area of the square = side² = √4761 x √4761 = 69 x 69 = 4761.
Therefore, the area of the square box is 4761 square units.
Problem 2
A square-shaped building measuring 4761 square feet is built; if each of the sides is √4761, what will be the square feet of half of the building?
2380.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4761 by 2, we get 2380.5.
So, half of the building measures 2380.5 square feet.
Problem 3
Calculate √4761 x 5.
345
Explanation
The first step is to find the square root of 4761, which is 69.
The second step is to multiply 69 by 5.
So, 69 x 5 = 345.
Problem 4
What will be the square root of (4624 + 137)?
The square root is 70.
Explanation
To find the square root, we need to find the sum of (4624 + 137). 4624 + 137 = 4761, and then √4761 = 69.
Therefore, the square root of (4624 + 137) is ±69.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √4761 units and the width 'w' is 38 units.
We find the perimeter of the rectangle as 214 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4761 + 38) = 2 × (69 + 38) = 2 × 107 = 214 units.
FAQ on Square Root of 4761
1.What is √4761 in its simplest form?
2.Mention the factors of 4761.
3.Calculate the square of 69.
4.Is 4761 a prime number?
5.4761 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 4761?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 4761?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 4761
- Square root: A square root is the inverse of a square. Example: 8² = 64, and the inverse of the square is the square root, that is √64 = 8.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 64 is a perfect square of 8.
- Prime factorization: The expression of a number as a product of its prime factors. Example: The prime factorization of 18 is 2 x 3 x 3.
- Integer: An integer is a whole number that can be positive, negative, or zero. Example: -2, 0, 3, 42 are integers.
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About BrightChamps in Oman
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
: He loves to play the quiz with kids through algebra to make kids love it.
