111 LearnersLast updated on May 26th, 2025
Square Root of 29.77
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 29.77
What is the Square Root of 29.77?
The square root is the inverse of the square of the number. 29.77 is not a perfect square. The square root of 29.77 is expressed in both radical and exponential form. In the radical form, it is expressed as √29.77, whereas (29.77)^(1/2) in the exponential form. √29.77 ≈ 5.456, 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 29.77
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 29.77 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 29.77, we consider it as 29.77.
Step 2: Now we need to find a number whose square is close to or less than 29. The number is 5 because 5 x 5 = 25. Now the quotient is 5, and the remainder is 4.
Step 3: Let us bring down 77, making the new dividend 477. Add the old divisor with the same number (5 + 5) to get 10, which will be our new divisor.
Step 4: The new divisor will be 10n, where we need to find the largest digit n such that 10n × n ≤ 477. In this case, n is 4 because 104 x 4 = 416.
Step 5: Subtract 416 from 477, and the remainder is 61. The quotient is now 5.4.
Step 6: Since the remainder is not zero, we need to continue the calculation. Add a decimal point, and bring down two zeroes to make it 6100.
Step 7: The new divisor becomes 108. Using the long division method, find the next digit.
Step 8: Continue these steps until you get a more precise value of the square root to the required decimal places.
The approximate square root of √29.77 is 5.456.
Square Root of 29.77 by Approximation Method
The approximation method is another method for finding square roots, and 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 29.77 using the approximation method.
Step 1: Now we have to find the closest perfect square to √29.77.
The smallest perfect square less than 29.77 is 25, and the largest perfect square greater than 29.77 is 36.
√29.77 falls somewhere between 5 and 6.
Step 2: Now we need to apply the formula:
(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)
Using this formula (29.77 - 25) ÷ (36 - 25) = 0.433.
Using the formula, we identified the decimal point of our square root.
The next step is adding the value we got initially to the decimal number which is 5 + 0.433 = 5.433, so the approximate square root of 29.77 is 5.433.
Common Mistakes and How to Avoid Them in the Square Root of 29.77
Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. 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 be taking 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.
Square Root of 29.77 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √29?
The area of the square is 29 square units.
Explanation
The area of the square = side^2.
The side length is given as √29.
Area of the square = side^2 = √29 x √29 = 5.385 x 5.385 ≈ 29
Therefore, the area of the square box is approximately 29 square units.
Problem 2
A square-shaped building measuring 29.77 square feet is built; if each of the sides is √29.77, what will be the square feet of half of the building?
Approximately 14.885 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 29.77 by 2 gives approximately 14.885.
So half of the building measures approximately 14.885 square feet.
Problem 3
Calculate √29.77 x 5.
Approximately 27.28
Explanation
The first step is to find the square root of 29.77, which is approximately 5.456.
The second step is to multiply 5.456 with 5. So 5.456 x 5 ≈ 27.28.
Problem 4
What will be the square root of (25 + 5)?
The square root is approximately 5.477
Explanation
To find the square root, we need to find the sum of (25 + 5). 25 + 5 = 30, and then √30 ≈ 5.477.
Therefore, the square root of (25 + 5) is approximately ±5.477.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √29.77 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as approximately 31.912 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√29.77 + 10) ≈ 2 × (5.456 + 10) = 2 × 15.456 ≈ 31.912 units.
FAQ on Square Root of 29.77
1.What is √29.77 in its simplest form?
2.What are the closest perfect squares to 29.77?
3.Calculate the square of 29.77.
4.Is 29.77 a perfect square?
5.What is the square root of 29.77 used for?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 29.77?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 29.77?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 29.77
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √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 has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Approximation: A method used to find an approximate value of a square root when an exact value is not easily obtainable.
- Long Division Method: A step-by-step method used to find the square root of non-perfect squares by dividing numbers in a structured manner.
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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.
