The product of two consecutive even numbers is 2208.what is the greater number?

To solve this problem, we need to understand that consecutive even numbers can be represented as x and x+2, where x is any even number.

Given that the product of two consecutive even numbers is 2208, we can set up the equation:

x(x + 2) = 2208

Solving this quadratic equation will give us the value of x, and then we can find the greater number by adding 2 to x.

Let's solve the equation:

x^2 + 2x - 2208 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, factoring is the easiest method.

The factors of 2208 that add up to 2 are 46 and 48. So, we can rewrite the equation as:

(x - 46)(x - 48) = 0

Setting each factor equal to zero gives the solutions x = 46 and x = 48.

Since we are looking for the greater number, the answer is 48.