Question

A binary operation * is defined on the set R, of real numbers by a * b = ab/4. Find the value of root 2 * root 6.

A. root 3
B. 3 root 2/4
C. root 3/2
D. root 2/2

Answer 1

To find the value of √2 * √6, first perform the binary operation by multiplying and then dividing by 4. Simplifying √12 reveals it equals 2√3, and dividing this by 4 results in √3/2, which is option C.

Step-by-step explanation:

The question is asking for the result of a binary operation * applied to the square roots of 2 and 6, where this operation is defined as a * b = ab/4 for any real numbers a and b. To find the value of √2 * √6, we multiply these two square roots and then divide by 4:

√2 * √6 = (√2 × √6) / 4 = √(2 × 6) / 4 = √12 / 4.

Now, simplify √12 by recognizing that 12 = 4 × 3, and since √4 is 2, we can write:

√12 = √(4 × 3) = √4 × √3 = 2√3.

Therefore, the final answer is:

(2√3) / 4 = √3 / 2.

This corresponds to option C from the provided options.