Select the correct answer.
What is this expression in simplified form?
[tex]$\frac{\sqrt{32}}{\sqrt{2}}$[/tex]
A. 16
B. 2
C. [tex]$\sqrt{30}$[/tex]
D. 4
Answer (2)
Use the property b a = b a to rewrite the expression as 2 32 .
Simplify the fraction inside the square root: 2 32 = 16 .
Evaluate the square root: 16 = 4 .
The simplified form of the expression is 4 .
Explanation
Understanding the problem We are asked to simplify the expression 2 32 . This involves simplifying a fraction with square roots in both the numerator and the denominator.
Using the property of square roots To simplify this expression, we can use the property that b a = b a . Applying this property, we get: 2 32 = 2 32
Simplifying the fraction Now, we simplify the fraction inside the square root: 2 32 = 16
Evaluating the square root So, our expression becomes: 16 Now, we evaluate the square root of 16: 16 = 4
Final Answer Therefore, the simplified form of the expression 2 32 is 4. The correct answer is D.
Examples
Imagine you are calculating the aspect ratio of a screen or a photograph. Aspect ratio is the ratio of the width to the height, and sometimes these dimensions involve square roots. Simplifying expressions like the one in this problem helps you find the simplest form of the ratio, making it easier to compare different screen sizes or photo formats. For instance, if one dimension involves 32 units and the other involves 2 units, simplifying the ratio 2 32 to 4 tells you that the width is 4 times the height.
The expression 2 32 simplifies to 4 by applying the property of square roots and simplifying the fraction inside. The correct answer is D. 4.
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