130 LearnersLast updated on May 26th, 2025
Square Root of 1/9
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 various fields like vehicle design, finance, etc. Here, we will discuss the square root of 1/9.
What is the Square Root of 1/9?
The square root is the inverse of the square of the number. 1/9 is a perfect square. The square root of 1/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(1/9), whereas (1/9)^(1/2) in exponential form. √(1/9) = 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 1/9
For perfect square numbers like 1/9, we can use direct methods such as simplification. Let us now learn the following methods:
- Simplification method
- Using properties of exponents
Square Root of 1/9 by Simplification Method
The simplification method involves expressing the number as a square of a simpler number. Let us look at how 1/9 is simplified:
Step 1: Express 1/9 as a square of a number. 1/9 = (1/3)²
Step 2: Take the square root of both sides. √(1/9) = √((1/3)²)
Step 3: The square root of (1/3)² is 1/3. So, √(1/9) = 1/3.
Square Root of 1/9 Using Properties of Exponents
Using properties of exponents is an efficient method for finding square roots. Let us learn how to find the square root of 1/9 using this method.
Step 1: Express 1/9 using exponents. 1/9 = (1/3)²
Step 2: Apply the exponent rule (a^m)^(1/n) = a^(m/n). (1/9)^(1/2) = ((1/3)²)^(1/2)
Step 3: Simplify the exponent. = (1/3)^(2/2) = (1/3)^1 = 1/3 Therefore, the square root of 1/9 is 1/3.
Common Mistakes and How to Avoid Them in the Square Root of 1/9
Students often make mistakes while finding the square root, such as forgetting to simplify the fraction. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting to Simplify the Fraction
It is important to simplify fractions before taking the square root. For instance, √(1/9) should be simplified to 1/3 rather than attempting to find a decimal approximation directly.
Mistake 2
Misapplying Square Root and Division
Confusing the square root with division can lead to errors. Ensure that the square root of a fraction is handled by finding the square root of the numerator and the denominator separately.
For example, √(1/9) = √1/√9 = 1/3.
Mistake 3
Ignoring the Properties of Exponents
Students may ignore exponent rules, which simplify calculations. Remember to apply (a^m)^(1/n) = a^(m/n) to simplify expressions involving exponents.
Mistake 4
Confusing the Square Root with the Cube Root
It's crucial to distinguish between square roots and cube roots, as they operate differently.
For example, √(1/9) is not the same as ∛(1/27).
Mistake 5
Neglecting Rational Numbers
Rational numbers like 1/3 should be identified and not approximated unnecessarily. Always express the square root of a rational number in its simplest form.
Square Root of 1/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(1/9)?
The area of the square is 1/9 square units.
Explanation
The area of the square = side².
The side length is given as √(1/9).
Area of the square = side²
= (1/3) x (1/3)
= 1/9.
Therefore, the area of the square box is 1/9 square units.
Problem 2
A square-shaped garden has an area of 1/9 square meters. What is the length of each side?
The length of each side is 1/3 meters.
Explanation
The area of a square is given by side².
Here, side² = 1/9.
To find the side length, take the square root of the area: √(1/9) = 1/3.
So, each side of the garden is 1/3 meters.
Problem 3
Calculate √(1/9) x 6.
2
Explanation
The first step is to find the square root of 1/9, which is 1/3.
The second step is to multiply 1/3 by 6. So, (1/3) x 6 = 2.
Problem 4
What will be the square root of (1/4 + 1/36)?
The square root is 1/2
Explanation
To find the square root, we first find the sum of (1/4 + 1/36). Convert to a common denominator: (9/36 + 1/36) = 10/36 = 5/18. Then, 5/18 is not a perfect square, so we approximate the square root. The approximate square root of 5/18 is not directly calculable, so further steps would involve approximation methods.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(1/9) meters and the width 'w' is 1 meter.
The perimeter of the rectangle is 2.67 meters.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/9) + 1)
= 2 × (1/3 + 1)
= 2 × (1.33)
= 2.67 meters.
FAQ on Square Root of 1/9
1.What is √(1/9) in its simplest form?
2.Is 1/9 a perfect square?
3.What is the square of 1/3?
4.Is √(1/9) a rational number?
5.Can a square root be negative?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1/9?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1/9?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 1/9
- Square root: A square root is the inverse of squaring. For example, 3² = 9, so the square root of 9 is 3. For 1/9, the square root is 1/3.
- Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers, and q ≠ 0. For example, 1/3 is a rational number.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 9 is a perfect square because it is 3². Similarly, 1/9 is a perfect square because it is (1/3)².
- Exponent: Exponents denote repeated multiplication of a number by itself. For example, (1/3)² means 1/3 multiplied by itself.
- Fraction: A fraction represents a part of a whole and is expressed as the ratio of two numbers, for example, 1/9.
Explore More algebra
About BrightChamps in United Kingdom
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.
