101 LearnersLast updated on May 26th, 2025
Square Root of 7.29
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7.29.
What is the Square Root of 7.29?
The square root is the inverse of the square of a number. 7.29 is a perfect square. The square root of 7.29 is expressed in both radical and exponential form. In the radical form, it is expressed as √7.29, whereas (7.29)^(1/2) in the exponential form. √7.29 = 2.7, 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 7.29
Different methods can be used to find the square root of a number, including the prime factorization method, long division method, and approximation method. However, since 7.29 is a perfect square, we can directly find its square root.
Square Root of 7.29 by Prime Factorization Method
The prime factorization method is usually used for integers, and since 7.29 is not an integer but a decimal, the prime factorization method is not applicable here. However, we know that 7.29 is a perfect square because 2.7 × 2.7 = 7.29, so the square root of 7.29 is 2.7.
Square Root of 7.29 by Long Division Method
The long division method can also be used to find the square root of decimal numbers. Here is a step-by-step method to find the square root of 7.29 using this method:
Step 1: Set up 7.29 for division. Group the numbers in pairs from the decimal point. Here, 7 and 29 are paired.
Step 2: Find the largest number whose square is less than or equal to the first group, which is 7. That number is 2, because 2 × 2 = 4.
Step 3: Subtract 4 from 7, which leaves a remainder of 3. Bring down 29, making the new dividend 329.
Step 4: Double the divisor (which is 2) to get 4 and place it as the beginning of the new divisor.
Step 5: Find a number, say x, such that 4x × x is less than or equal to 329. The number is 7, because 47 × 7 = 329.
Step 6: Subtract 329 from 329 to get 0. The quotient, 2.7, is the square root of 7.29.
Square Root of 7.29 by Approximation Method
Since 7.29 is a perfect square, the approximation method is not necessary. Using the approximation method typically involves identifying the closest perfect squares around the number and estimating, but since we know 2.7 × 2.7 = 7.29, the square root is exactly 2.7.
Common Mistakes and How to Avoid Them in the Square Root of 7.29
Students may make errors while finding the square root, such as overlooking the negative square root or misplacing the decimal point. Here, we address 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. However, we usually consider only the positive square root for practical purposes.
For example, √7.29 = 2.7, but -2.7 is also a square root.
Square Root of 7.29 Examples
Problem 1
What is the area of a square if its side length is √7.29?
The area of the square is 7.29 square units.
Explanation
The area of a square is given by side².
The side length is given as √7.29, which is 2.7.
Therefore, the area = (2.7)² = 7.29 square units.
Problem 2
A square-shaped garden has an area of 7.29 square meters. What is the length of each side?
Each side of the garden is 2.7 meters.
Explanation
The length of each side is the square root of the area.
Since the area is 7.29 square meters, each side is √7.29 = 2.7 meters.
Problem 3
Calculate 5 times the square root of 7.29.
The result is 13.5.
Explanation
First, find the square root of 7.29, which is 2.7.
Then multiply 2.7 by 5: 2.7 × 5 = 13.5.
Problem 4
What is the square root of (7.29 + 9)?
The square root is 4.
Explanation
First, find the sum of 7.29 + 9 = 16.
Then find the square root of 16, which is 4.
Therefore, the square root of (7.29 + 9) is ±4.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √7.29 units and the width ‘w’ is 5 units.
The perimeter of the rectangle is 15.4 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Length = √7.29 = 2.7 units.
Perimeter = 2 × (2.7 + 5) = 2 × 7.7 = 15.4 units.
FAQ on Square Root of 7.29
1.What is √7.29 in its simplest form?
2.What are the factors of 7.29?
3.Calculate the square of 7.29.
4.Is 7.29 a perfect square?
5.What is 7.29 divisible by?
Important Glossaries for the Square Root of 7.29
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.
- Rational number: A rational number is a number that can be expressed as the quotient of two integers, where the denominator is not zero.
- Perfect square: A perfect square is a number that is the square of an integer or a rational number. Example: 4, 9, and 7.29 are perfect squares.
- Decimal number: A decimal number has a whole number part and a fractional part separated by a decimal point. Example: 2.7, 3.14.
- Long division method: A method used to find the square root of numbers, especially non-perfect squares, by performing division iteratively.
Explore More algebra
Previous to Square Root of 7.29
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.
