Question
Identify the most simplified version of the expression below: \[ \begin{array}{ll}\frac{18 \sqrt{5}}{\sqrt{3}} \\ \text { A) } 15 \sqrt{15} & \text { C) } \frac{8 \sqrt{15}}{3} \\ \text { B) } 6 \sqrt{15} & \text { D) } 2 \sqrt{15}\end{array} \]
Ask by Gibbs Chandler. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The most simplified version is \( 6\sqrt{15} \), choice B.
Solution
We start with the expression (18√5)/√3. To simplify, multiply the numerator and denominator by √3 to rationalize the denominator:
(18√5/√3) × (√3/√3) = (18√5√3)/(√3√3).
Since √5√3 = √15 and √3√3 = 3, the expression becomes:
(18√15)/3.
Finally, divide 18 by 3 to get:
6√15.
So, the most simplified version is 6√15, which corresponds to answer B.
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{18 \sqrt{5}}{\sqrt{3}} \), we start by rationalizing the denominator: 1. Multiply the numerator and the denominator by \( \sqrt{3} \): \[ \frac{18 \sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{18 \sqrt{15}}{3} \] 2. Now simplify \( \frac{18}{3} = 6 \): \[ = 6 \sqrt{15} \] So, the most simplified version of the expression is \( 6 \sqrt{15} \). The correct answer is B) \( 6 \sqrt{15} \).
