103 LearnersLast updated on May 26th, 2025
Square Root of 5929
If a number is multiplied by the same number, the result is a square. The inverse operation is finding the square root. Square roots are used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 5929.
What is the Square Root of 5929?
The square root is the inverse of the square of a number. 5929 is a perfect square. The square root of 5929 is expressed in both radical and exponential form. In radical form, it is expressed as √5929, whereas in exponential form, it is (5929)^(1/2). √5929 = 77, 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 5929
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, 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 5929 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Let us look at how 5929 is broken down into its prime factors.
Step 1: Finding the prime factors of 5929 Breaking it down, we get 7 x 7 x 11 x 11: 7² x 11²
Step 2: Now that we found the prime factors of 5929, we can pair them since 5929 is a perfect square.The square root of 5929 is the product of one number from each pair: 7 x 11 = 77.
Square Root of 5929 by Long Division Method
The long division method is used for both perfect and non-perfect square numbers. Let us learn how to find the square root using the long division method, step by step.
Step 1: Group the numbers from right to left. In the case of 5929, group it as 59 and 29.
Step 2: Find n whose square is less than or equal to 59. We choose n as 7 because 7 x 7 = 49, which is less than 59. The quotient is 7. Subtract 49 from 59 to get a remainder of 10.
Step 3: Bring down 29, making the new dividend 1029. Double the quotient (7) to get 14, which is part of the new divisor.
Step 4: Find a digit x such that 14x x x is less than or equal to 1029. The suitable digit is 7, as 147 x 7 = 1029.
Step 5: Subtract 1029 from 1029, resulting in a remainder of 0. The quotient is 77.
So the square root of √5929 is 77.
Square Root of 5929 by Approximation Method
The approximation method is another method for finding square roots and is useful for non-perfect squares. Let's look at how it applies to the square root of 5929, even though this number is a perfect square.
Step 1: Identify two perfect squares between which 5929 falls. However, since 5929 is a perfect square, we already know the exact square root is 77.
Step 2: If not a perfect square, you would use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) to find an approximate decimal. This step is unnecessary for perfect squares like 5929.
Since 5929 is perfect, the square root is exactly 77.
Common Mistakes and How to Avoid Them in the Square Root of 5929
Students make mistakes while finding square roots, such as forgetting about negative square roots or skipping long division steps. Let us explore a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. Usually, we consider only the positive square root.
For example: √5929 = 77, but there is also -77 which should not be forgotten.
Square Root of 5929 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √529?
The area of the square is 529 square units.
Explanation
The area of the square = side².
The side length is given as √529.
Area of the square = side² = √529 x √529 = 23 × 23 = 529
Therefore, the area of the square box is 529 square units.
Problem 2
A square-shaped building measuring 5929 square feet is built; if each of the sides is √5929, what will be the square feet of half of the building?
2964.5 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 5929 by 2 gives us 2964.5.
So half of the building measures 2964.5 square feet.
Problem 3
Calculate √5929 x 5.
385
Explanation
The first step is to find the square root of 5929, which is 77.
The second step is to multiply 77 by 5.
So 77 x 5 = 385.
Problem 4
What will be the square root of (529 + 400)?
The square root is 29.
Explanation
To find the square root, we need to find the sum of (529 + 400). 529 + 400 = 929, and then √929 ≈ 30.479.
Therefore, the square root of (529 + 400) is approximately ±30.479.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √529 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 122 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√529 + 38) = 2 × (23 + 38) = 2 × 61 = 122 units.
FAQ on Square Root of 5929
1.What is √5929 in its simplest form?
2.Mention the factors of 5929.
3.Calculate the square of 77.
4.Is 5929 a perfect square?
5.Is 5929 a prime number?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 5929?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 5929?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 5929
- Square root: A square root is a number that, when multiplied by itself, gives the original number. Example: 7² = 49, so √49 = 7.
- Rational number: A rational number can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero.
- Perfect square: A perfect square is an integer that is the square of another integer. Example: 36 is a perfect square because it is 6².
- Prime factorization: Expressing a number as a product of its prime factors. Example: 84 = 2² x 3 x 7.
- Long division method: A technique to find square roots by division, useful for both perfect and 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
: He loves to play the quiz with kids through algebra to make kids love it.
