Final answer:
To satisfy the equation √(648) = √(2^a•3^b), we factorize 648 and find its prime factors raised to the proper exponents that equate to the square root of each side. The correct values are a=3 and b=4, as per option c).
Step-by-step explanation:
To find the values of a and b that make the equation √(648) = √(2a•3b) true, we need to simplify both sides of the equation and match them accordingly. We begin by simplifying the left-hand side:
- Square root of 648 can be factorized to 23 • 34 which is 2 • 2 • 2 • 3 • 3 • 3 • 3.
- Taking the square root of this, we are left with 23/2 • 34/2.
- √(648) simplifies to 21.5 • 32.
Comparing this to the right-hand side √(2a•3b), we can see that:
- a must be 3, because 21.5 is the square root of 23.
- b must be 4, because 32 is the square root of 34.
Therefore, the correct option answer in the final answer is c) a=3, b=4.
There is no need to consider the irrelevant information provided about solving quadratic equations since it does not apply to finding the values of a and b here.