Which is equal to $\sqrt{0.09}$?
A. $\frac{3}{10}$
B. $\frac{1}{9}$
C. $\frac{1}{3}$
D. $\frac{3}{100}$
Answer (2)
Convert 0.09 to a fraction: 0.09 = 100 9 .
Take the square root: 0.09 = 100 9 .
Simplify the square root: 100 9 = 100 9 = 10 3 .
The answer is 10 3 .
Explanation
Understanding the problem We are asked to find the value of 0.09 among the given options: 10 3 , 9 1 , 3 1 , 100 3 .
Converting to a fraction First, let's convert 0.09 to a fraction. We have 0.09 = 100 9 .
Taking the square root Now, let's find the square root of this fraction: 0.09 = 100 9 .
Rewriting the square root We can rewrite the square root of a fraction as a fraction of square roots: 100 9 = 100 9 .
Simplifying Now, we simplify the square roots: 100 9 = 10 3 .
Direct Calculation Alternatively, we can directly calculate the square root of 0.09, which is 0.3. Converting 0.3 to a fraction, we get 0.3 = 10 3 .
Final Answer Comparing our result with the given options, we see that 0.09 = 10 3 .
Examples
Understanding square roots is crucial in many real-world applications, such as calculating distances or areas. For example, if you have a square garden with an area of 0.09 square meters, finding the side length involves calculating the square root of 0.09, which is 0.3 meters. This concept is also used in physics to determine velocities and accelerations, and in finance to calculate investment growth rates. Mastering square roots helps in making informed decisions in various practical scenarios.
The square root of 0.09 is found to be 10 3 by converting it to a fraction and simplifying. Therefore, the correct choice is option A. The calculation shows that 0.09 = 10 3 .
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