101 LearnersLast updated on May 26th, 2025
Square Root of 2.89
If a number is multiplied by itself, the result is a square. The inverse operation of squaring a number is finding its square root. Square roots are used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 2.89.
What is the Square Root of 2.89?
The square root is the inverse of squaring a number. 2.89 is a perfect square. The square root of 2.89 can be expressed in both radical and exponential form. In radical form, it is expressed as √2.89, whereas in exponential form, it is expressed as (2.89)^(1/2). The square root of 2.89 is 1.7, 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 2.89
There are multiple methods to find the square root of a number. Since 2.89 is a perfect square, we can use the prime factorization method; however, for non-perfect squares, methods like long division or approximation are typically used. Let us look into these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2.89 by Prime Factorization Method
Prime factorization is typically used for perfect square integers. However, for decimal numbers like 2.89, we recognize it as a perfect square directly.
Step 1: Recognize that 2.89 can be expressed as (1.7 x 1.7).
Therefore, the square root of 2.89 using prime factorization is straightforward as 1.7.
Square Root of 2.89 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also verify the square root of perfect squares. Here’s how you would approach it for 2.89:
Step 1: Group the digits of 2.89 from right to left, giving us 2 and 89.
Step 2: Find a number whose square is less than or equal to 2, which is 1. Subtract 1^2 = 1 from 2, leaving a remainder of 1.
Step 3: Bring down 89 to get 189.
Step 4: Double the divisor from step 2, which is 1, making it 2. Find a digit x such that 2x * x is less than or equal to 189. The number x is 7 since 27 * 7 = 189.
Thus, the square root of 2.89 is confirmed to be 1.7.
Square Root of 2.89 by Approximation Method
Approximation is useful for estimating square roots of non-perfect squares. However, it can also confirm perfect squares. Here's how it can be applied to 2.89:
Step 1: Recognize that 2.89 is close to 3 and 2.25, the squares of 1.5 and 1.7, respectively.
Step 2: Use the proximity of 2.89 to 2.25 to conclude that its square root is approximately 1.7.
Thus, the square root of 2.89 is 1.7.
Common Mistakes and How to Avoid Them in the Square Root of 2.89
Students often make mistakes when finding square roots, such as ignoring the negative square root, skipping steps in the long division method, etc. Let us examine some common errors 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 often take only the positive square root, as it is the most relevant in many real-world applications.
For example, while √2.89 = 1.7, there is also -1.7, which should not be ignored.
Square Root of 2.89 Examples
Problem 1
Can you help Max find the perimeter of a square if its side length is √2.89?
The perimeter of the square is 6.8 units.
Explanation
The perimeter of a square = 4 × side.
The side length is given as √2.89 = 1.7.
Perimeter = 4 × 1.7 = 6.8 units.
Problem 2
A square-shaped garden has an area of 2.89 square meters. What is the length of one side of the garden?
The length of one side of the garden is 1.7 meters.
Explanation
Since the area of the garden is 2.89 square meters, the side length is √2.89.
Therefore, the side length is 1.7 meters.
Problem 3
Calculate √2.89 × 4.
6.8
Explanation
First, find the square root of 2.89, which is 1.7.
Then multiply 1.7 by 4. So, 1.7 × 4 = 6.8.
Problem 4
What will be the square root of (2.5 + 0.39)?
The square root is approximately 1.7.
Explanation
To find the square root, we need to find the sum of (2.5 + 0.39). 2.5 + 0.39 = 2.89, and then √2.89 = 1.7.
Therefore, the square root of (2.5 + 0.39) is ±1.7.
Problem 5
Find the diagonal of a square if each side is √2.89 meters long.
The diagonal of the square is approximately 2.4 meters.
Explanation
The diagonal of a square = side × √2.
Diagonal = 1.7 × 1.414 (approximately) = 2.4 meters.
FAQ on Square Root of 2.89
1.What is √2.89 in its simplest form?
2.What are the factors of 2.89?
3.Calculate the square of 2.89.
4.Is 2.89 a prime number?
5.2.89 is divisible by?
Important Glossaries for the Square Root of 2.89
- Square root: A square root is the inverse of a square. Example: 1.7² = 2.89, and the inverse of the square is the square root, which is √2.89 = 1.7.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not zero, and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 2.89 is a perfect square because it equals 1.7 squared.
- Decimal: A decimal is a number that includes a whole number and a fractional part, separated by a decimal point. Examples include 2.89, 3.5, etc.
- Precision: Precision refers to the accuracy of a number, particularly in terms of its decimal representation. For example, the square root of 2.89 is precisely 1.7.
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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.
