Which expression is equivalent to the given expression?$\frac{9}{\sqrt{10}}$
A. $3 \sqrt{10}$
B. $\frac{9 \sqrt{10}}{10}$
C. 9
D. $\frac{3}{\sqrt{10}}$
Answer (2)
The problem requires finding an expression equivalent to 10 9 .
Rationalize the denominator by multiplying both numerator and denominator by 10 .
This gives 10 9 10 .
The equivalent expression is 10 9 10 .
Explanation
Understanding the Problem We are given the expression 10 9 and asked to find an equivalent expression from the options provided. The key here is to rationalize the denominator.
Rationalizing the Denominator To rationalize the denominator, we multiply both the numerator and the denominator by 10 : 10 9 × 10 10 = 10 9 10
Comparing with Options Now we compare the result 10 9 10 with the given options:
A. 3 10
B. 10 9 10
C. 9
D. 10 3
We see that option B matches our simplified expression.
Final Answer Therefore, the expression equivalent to 10 9 is 10 9 10 .
Examples
Rationalizing the denominator is a useful technique in various fields, such as physics and engineering, where you might encounter expressions with radicals in the denominator. For example, when calculating impedance in electrical circuits or dealing with wave functions in quantum mechanics, simplifying expressions by rationalizing denominators can make calculations easier and more accurate. Imagine you are designing a bridge and need to calculate the stress on a support beam. If your stress calculation involves a fraction with a square root in the denominator, rationalizing it will help you get a more precise and manageable result.
The equivalent expression to 10 9 is found by rationalizing the denominator, which results in 10 9 10 . Among the provided options, the correct answer is B: 10 9 10 .
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