Final answer:
The expression 6√27/4√3 simplifies to 9/2 by breaking down the square roots and canceling out common factors.
Step-by-step explanation:
The expression 6√27/4√3 can be simplified by factoring out the square roots and reducing the expression. First, we simplify the square root of 27 by recognizing it as √(9•3), which simplifies to 3√3. The square root of 3 is already in its simplest form. Therefore, we can rewrite the original expression as (6•3√3)/4√3.
Next, we can simplify the expression by canceling out common factors. The √3 terms in the numerator and the denominator will cancel each other out, and 6 divided by 4 reduces to 3/2 when simplified. The final simplified form of the expression is 9/2, since 3•3/2=9/2.
This process demonstrates how to deal with square roots and fractions in algebraic expressions. Performing such simplifications is necessary to solve equations with one variable and to understand the properties of exponents and radicals.