What is the following quotient?
$\frac{\sqrt{120}}{\sqrt{30}}$
Answer (2)
The quotient 30 120 simplifies to 2. By using the property of square roots, we determined that 30 120 = 4 , and the square root of 4 is 2.
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The final answer is 2
Examples
Imagine you're comparing the speeds of two runners on different tracks. One track is 120 meters long, and the other is 30 meters long. If both runners cover their respective tracks in the same amount of time, the ratio of their speeds can be represented as 30 120 . Simplifying this expression, we find that the runner on the 120-meter track is twice as fast as the runner on the 30-meter track. This concept of simplifying quotients of square roots is useful in various fields, such as physics, engineering, and computer science, for comparing rates, scaling quantities, and analyzing data.
