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?
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.
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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.
