Square Root of 1.69
2026-02-28 08:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1.69

426 Learners

Last updated on August 5, 2025

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.

Explore Our Programs

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √1.69?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √1.69 × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (0.69 + 1)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length 'l' is √1.69 units and the width 'w' is 0.3 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1.69

1.What is √1.69 in its simplest form?

The simplest form of √1.69 is 1.3.

2.Can 1.69 be expressed as a fraction?

Yes, 1.69 can be expressed as 169/100.

3.Calculate the square of 1.69.

To find the square of 1.69, multiply it by itself: 1.69 × 1.69 = 2.8561.

4.Is 1.69 a rational number?

Yes, 1.69 is a rational number because it can be expressed as the fraction 169/100.

5.What is the decimal representation of the square root of 1.69?

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.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.