102 LearnersLast updated on May 26th, 2025
Square Root of 1.69
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 1.69
What is the Square Root of 1.69?
The square root is the inverse of the square of the number. 1.69 is a perfect square. The square root of 1.69 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1.69, whereas (1.69)^(1/2) in the exponential form. √1.69 = 1.3, 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 1.69
The prime factorization method is typically used for perfect square numbers. Since 1.69 is a perfect square, we can use simple arithmetic to find its square root. Other methods like the long-division method and approximation are not needed in this case. Let us now learn how we can find the square root:
- Arithmetic method
- Verification method
Square Root of 1.69 by Arithmetic Method
By simple arithmetic, we can determine that 1.69 is the square of 1.3.
Step 1: Recognize the decimal nature of 1.69 and express it as a fraction: 1.69 = 169/100.
Step 2: Simplify the expression by taking the square root of both the numerator and the denominator: √(169/100) = √169 / √100 = 13/10 = 1.3.
Thus, the square root of 1.69 is 1.3.
Square Root of 1.69 by Verification Method
Verification ensures the correctness of our arithmetic approach. By squaring 1.3, we can validate our result.
Step 1: Square 1.3 to verify: 1.3 × 1.3 = 1.69.
Step 2: Since our squared result is 1.69, the square root of 1.69 is indeed 1.3.
Common Mistakes and How to Avoid Them in the Square Root of 1.69
Students do make mistakes while finding the square root, such as forgetting about the negative square root or miscalculating decimal places. 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 has both positive and negative square roots. However, typically only the principal (positive) square root is considered in practical applications.
For example, √1.69 = 1.3, but there is also -1.3, which should not be forgotten.
Square Root of 1.69 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.69?
The area of the square is 1.69 square units.
Explanation
The area of the square = side^2.
The side length is given as √1.69.
Area of the square = side^2 = √1.69 × √1.69 = 1.3 × 1.3 = 1.69.
Therefore, the area of the square box is 1.69 square units.
Problem 2
A square-shaped garden measures 1.69 square meters; if each of the sides is √1.69, what will be the square meters of half of the garden?
0.845 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 1.69 by 2 = 0.845
So half of the garden measures 0.845 square meters.
Problem 3
Calculate √1.69 × 5.
6.5
Explanation
The first step is to find the square root of 1.69, which is 1.3.
The second step is to multiply 1.3 with 5.
So 1.3 × 5 = 6.5.
Problem 4
What will be the square root of (0.69 + 1)?
The square root is 1.3.
Explanation
To find the square root, we need to find the sum of (0.69 + 1).
0.69 + 1 = 1.69, and then √1.69 = 1.3.
Therefore, the square root of (0.69 + 1) is ±1.3.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1.69 units and the width 'w' is 0.3 units.
We find the perimeter of the rectangle as 3.2 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.69 + 0.3)
= 2 × (1.3 + 0.3)
= 2 × 1.6
= 3.2 units.
FAQ on Square Root of 1.69
1.What is √1.69 in its simplest form?
2.Can 1.69 be expressed as a fraction?
3.Calculate the square of 1.69.
4.Is 1.69 a rational number?
5.What is the decimal representation of the square root of 1.69?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 1.69?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 1.69?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 1.69
- Square root: A square root is the inverse of a square. For example, 1.3^2 = 1.69, and thus the square root of 1.69 is 1.3.
- Rational number: A rational number can be expressed as the quotient of two integers, where the denominator is not zero. For example, 1.3 is rational because it is 13/10.
- Perfect square: A number that is the square of an integer or a rational number. For example, 1.69 is a perfect square because it is (1.3)^2.
- Decimal: A number that has a whole number and a fractional part separated by a decimal point, such as 1.3.
- Principal square root: The non-negative square root of a number. For instance, the principal square root of 1.69 is 1.3.
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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.
