Select the correct answer.
What is this expression in simplified form?
$\frac{\sqrt{6}}{\sqrt{23}}$
A. $\frac{\sqrt{138}}{\sqrt{23}}$
B. $\frac{\sqrt{14}}{21}$
C. $\frac{\sqrt{138}}{23}$
D. $\frac{14 \sqrt{3}}{7}$
Answer (1)
Rationalize the denominator by multiplying both numerator and denominator by 23 .
Simplify the expression: 23 6 × 23 23 = 23 138 .
Compare the simplified expression with the given options.
The correct answer is 23 138 .
Explanation
Understanding the Problem We are given the expression 23 6 and asked to simplify it and choose the correct answer from the given options.
Rationalizing the Denominator To simplify this expression, we need to rationalize the denominator. This means we want to eliminate the square root from the denominator. We can do this by multiplying both the numerator and the denominator by 23 .
Simplifying the Expression Multiplying the numerator and denominator by 23 , we get: 23 6 × 23 23 = 23 × 23 6 × 23 = 23 6 × 23 = 23 138 So, the simplified expression is 23 138 .
Selecting the Correct Answer Now we compare our simplified expression with the given options: A. 23 138 B. 21 14 C. 23 138 D. 7 14 3 Our simplified expression 23 138 matches option C.
Final Answer Therefore, the correct answer is C. 23 138 .
Examples
Rationalizing the denominator is a useful technique in various fields, such as physics and engineering, where simplified expressions are crucial for calculations. For example, when calculating impedance in electrical circuits, you might encounter complex numbers with square roots in the denominator. Rationalizing the denominator makes it easier to perform further calculations and comparisons.
